Image forming state adjusting system, exposure method and exposure apparatus, and program and information storage medium

ABSTRACT

A second communications server obtains adjustment information of an adjustment unit in an exposure apparatus and information related to image forming quality (such as wavefront aberration) of a projection optical system under an exposure condition that serves as a reference, via a first communications server, and then calculates an optimal adjustment amount of the adjustment unit under a target exposure condition based on the information. In addition, the second communications server obtains adjustment information of the adjustment and actual measurement data of image forming quality of the projection optical system via the first communications server, and then calculates the optimal adjustment amount of the adjustment unit under the target exposure condition based on the information. And, the second communications server controls the adjustment unit in the exposure apparatus via the first communications server, based on the calculations results.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No. 10/901,209filed Jul. 29, 2004 now U.S. Pat. No. 7,230,682, which is a continuationof International Application PCT/JP2003/000833 with an internationalfiling date of Jan. 29, 2003, which was not published in English. Theentire contents of those applications are hereby incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to image forming state adjusting systems,exposure methods and exposure apparatus, and programs and informationstorage mediums, and more particularly, to an image forming stateadjusting system that optimizes the image forming state of a pattern bya projection optical system used in an exposure apparatus, an exposuremethod and an exposure apparatus that can actually achieve theoptimization of the image forming state, and a program that makes acomputer execute optimizing the image forming state of the pattern inthe exposure apparatus and an information storage medium in which theprogram is stored.

2. Description of the Related Art

Conventionally, when manufacturing devices such as semiconductors,liquid crystal displays, or the like in a photolithographic process,projection exposure apparatus such as a reduction projection exposureapparatus based on a step-and-repeat method (a so-called stepper) and ascanning projection exposure apparatus based on a step-and-scan method(a so-called scanning stepper) have been used. Such exposure apparatustransfer a pattern of a photomask or a reticle (hereinafter generallyreferred to as a ‘reticle’) onto a substrate such as a wafer or a glassplate on which a photosensitive agent such as a photoresist is coated,via a projection optical system.

When manufacturing devices such as a semiconductor, because differentcircuit patterns have to be formed overlaid on the substrate in multiplelayers, it is important to accurately overlay the pattern formed on thereticle and the pattern already formed on each shot area on the wafer.In order to perform such overlay with good accuracy, it is absolutelynecessary for the image forming quality of the projection optical systemto be adjusted to a desired state (for example, a magnification error ofa transferred image of a reticle pattern to a shot area (pattern) on asubstrate is corrected). Even in the case of transferring a reticlepattern of the first layer to each shot area on the substrate, the imageforming quality of the projection optical system is preferably adjustedso that the reticle pattern of the second layer and onward istransferred with good precision on each shot area.

As a premise for adjusting the image forming quality (one of the opticalproperties) of the projection optical system, the image forming qualityhas to be accurately measured (or detected). As a measuring method ofthe image forming quality, a method in which the image forming quality,or to be more specific, Seidel's five aberrations (distortion, sphericalaberration, astigmatism, field curvature and coma) is calculated(hereinafter referred to as ‘exposing method’), is mainly used. In thisexposing method, exposure is performed using a measurement reticle onwhich a predetermined measurement pattern is formed, then thetransferred image obtained by developing the substrate where the imageof the measurement pattern is projected and formed, such as the resistimage, is measured, and then the image forming quality is calculatedbased on the measurement results. Besides such a method, a method inwhich the above-mentioned five aberrations are calculated withoutactually performing exposure (hereinafter referred to as an ‘aerialimage measurement method’) is also used. In this method, a measurementreticle is illuminated with an illumination light, and aerial images(projected images) of measurement patterns formed by the projectionoptical system are measured, and then the above five aberrationscalculated based on the measurement results.

However, with the above exposing method or aerial image measurementmethod, in order to obtain all five aberrations, the measurement has tobe repeated separately, using the appropriate pattern for eachmeasurement. Furthermore, depending on the type and amount of theaberration to be measured, the order in which the measurement isperformed has to be considered, in order to accurately adjust theprojection optical system. For example, when coma is large, the image ofthe pattern is not resolved, therefore, when aberration such asdistortion, spherical aberration, astigmatism are measured in thisstate, accurate data cannot be obtained. Accordingly, distortion or thelike has to be measured, after the coma has been reduced to a certainlevel.

In addition, due to higher integration of semiconductor devices or thelike in recent years, circuit patterns are becoming finer, which makescorrection of only the Seidel's five aberrations insufficient, andrequirements are pressing for an overall adjustment, including thehigher order of aberrations, in the image forming quality of theprojection optical system. In order to perform such overall adjustmentin the image forming quality, a light-ray-trace computation has to beperformed using data (such as curvature, refractive index, andthickness) of individual lens elements composing the projection opticalsystem, to identify the lens element that requires adjustment and tocalculate its adjustment amount.

However, because data of individual lens elements are confidential forthe exposure apparatus maker, it is usually difficult for a servicetechnician repairing or adjusting the exposure apparatus or a user toobtain such data. In addition, since the light-ray-trace computationrequires an enormous amount of time, it is not realistic for the servicetechnician to perform the computation on site.

In addition, to adjust the image forming quality or the image formingstate of the projection optical system, for example, an image formingquality adjustment mechanism or the like that adjusts the position andthe inclination of the optical elements such as lens elements making upthe projection optical system is used. However, the image formingquality changes depending on exposure conditions such as illuminationconditions (such as illumination σ), N.A. (numerical aperture) of theprojection optical system, and the pattern to be used. Accordingly, theoptimal adjustment position of each optical element by the image formingquality adjustment mechanism under a certain exposure condition may notnecessarily be the optimal adjustment position under other exposureconditions.

Against such background, a new system was expected that could smoothlycalculate adjustment position of each optical element by the imageforming quality adjustment mechanism that brings out the optimal imageforming quality under any exposure condition, such as the combination ofN.A. of the projection optical system, illumination σ, and the subjectpattern.

SUMMARY OF THE INVENTION

The present invention has been made under such circumstances, and has asits first object to provide an image forming state optimizing systemthat can smoothly optimize the forming state of a projected image of apattern on an object under any targeted exposure conditions.

The second object of the present invention is to provide an exposuremethod and an exposure apparatus that can optimize the forming state ofa projected image of a pattern on an object and transfer the patternwith good accuracy onto the object under any targeted exposureconditions.

In addition, the third object of the present invention is to provide aprogram that makes a computer structuring a part of a control system ofthe exposure apparatus execute a process of smoothly optimizing theforming state of a projected image of a pattern on an object, and toprovide an information storage unit.

According to a first aspect of the present invention, there is provideda first image forming state adjusting system used in an exposureapparatus, which forms a projected image of a predetermined pattern onan object using a projection optical system, the system being a systemthat optimizes a forming state of the projected image on the object,comprising: an adjustment unit that adjusts a forming state of theprojected image on the object; and a computer that connects to theexposure apparatus via a communication channel and calculates an optimaladjustment amount of the adjustment unit under a target exposurecondition, using adjustment information of the adjustment unit andinformation related to image forming quality of the projection opticalsystem under a predetermined exposure condition.

In this description, ‘exposure condition’ refers to conditions relatedto exposure that are decided by combining illumination conditions (suchas illumination σ (coherence factor), annular ratio, or dosedistribution on a pupil plane of an illumination optical system),numerical aperture (N.A.) of the projection optical system, and the typeof pattern (such as, whether the pattern is an extracted pattern or aresidual pattern, a dense pattern or an isolated pattern; in the case ofa line-and-space pattern, its pitch, line width, and duty ratio, and inthe case of an isolated pattern, its line width. Or, in the case ofcontact holes, its longitudinal length, its lateral length, and thelength between the hole patterns (such as its pitch), or whether thepattern is a phase shift pattern or not, or whether the projectionoptical system has a pupil filter or not.)

According to this system, the computer calculates the optimal adjustmentamount of the adjustment unit under the target exposure condition usingadjustment information of the adjustment unit and information related toimage forming quality of the projection optical system under apredetermined exposure condition. That is, because the relation betweenthe adjustment information of the adjustment unit and the informationrelated to image forming quality of the projection optical system(aberration) under a predetermined exposure condition is well known, theoptimal adjustment amount of the image forming quality of the projectionoptical system under the predetermined exposure condition can be easilyfound. Accordingly, the optimal adjustment amount under the targetexposure condition that is calculated using such adjustment informationof the adjustment unit and information related to image forming qualityof the projection optical system under the predetermined exposurecondition is highly precise. Therefore, by adjusting the adjustment unitbased on the adjustment amount, the forming state of the projected imageof the pattern on the object under any target exposure condition can besmoothly optimized.

In this case, for example, the predetermined exposure condition can beat least one reference exposure condition. In such a case, as thepredetermined exposure condition, at least one reference exposurecondition can be decided whose adjustment amount for optimally adjustingthe image forming quality of the projection optical system is obtainedin advance. And, when the optimal adjustment amount under the targetexposure condition is calculated using the adjustment information of theadjustment unit and information related to image forming quality of theprojection optical system under such reference exposure condition, thecalculated optimal adjustment amount is highly precise.

In this case, the information related to image forming quality mayinclude various kinds of information so long as it is a base forcalculating the optimal adjustment amount of the adjustment unit underthe target exposure condition, as is with the adjustment information.For example, the information related to image forming quality caninclude information on wavefront aberration of the projection opticalsystem that has been adjusted under the reference exposure condition.Or, the information related to image forming quality can includeinformation on a stand-alone wavefront aberration of the projectionoptical system and image forming quality of the projection opticalsystem under the reference exposure condition. In the latter case, giventhat the deviation between the wavefront aberration of the projectionoptical system itself (for example, before the projection optical systemis assembled into the exposure apparatus) (stand-alone wavefrontaberration) and the wavefront aberration of the projection opticalsystem in an on-body state (that is, after the projection optical systemis assembled into the exposure apparatus) after adjustment under thereference exposure condition corresponds to the deviation of theadjustment amount of the adjustment unit, a correction amount of theadjustment amount can be calculated based on the deviation from an idealstate of image forming quality, and based on such correction amount, thecorrection amount of the wavefront aberration can be obtained. Then,based on the correction amount of the wavefront aberration, thestand-alone wavefront aberration, and information on wavefrontaberration variation values of the adjustment unit, which is apositional reference of the adjustment unit under the reference exposurecondition, the wavefront aberration of the projection optical systemafter adjustment under the reference exposure condition can be obtained.

With the first image forming state adjusting system in the presentinvention, the information related to image forming quality of theprojection optical system can be information on a difference betweenimage forming quality of the projection optical system under thereference exposure condition and a predetermined target value of theimage forming quality, and the adjustment information of the adjustmentunit can be information on an adjustment amount of the adjustment unit,and in this case, the computer can calculate the optimal adjustmentamount using a relation expression between the difference, a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system and coefficients of each term in aZernike polynomial under the target exposure condition, a wavefrontaberration variation table made up of parameters that denotes a relationbetween adjustment of the adjustment unit and a change in wavefrontaberration of the projection optical system, and the adjustment amount.

A predetermined target value of the image forming quality, in this case,includes the case when the target value of the image forming quality(such as aberration) is zero.

In this case, for example, the predetermined target value can be atarget value of image forming quality in at least one evaluation pointof the projection optical system that has been input externally.However, when the target value is not given in particular for thepredetermined target value, it can be set to zero.

In this case, the target value of image forming quality can be a targetvalue of image forming quality at a chosen representative point. Or, thetarget value of image forming quality can be a target value of imageforming quality whose target value of a coefficient is converted, thetarget value of the coefficient being set by decomposing the imageforming quality of the projection optical system into components by anaberration decomposition method and improving a faulty component basedon a decomposition coefficient obtained by the decomposition.

With the image forming state adjusting system in the present invention,for the computer to calculate the optimal adjustment amount, therelation expression can be an equation that includes a weightingfunction to perform weighting on any terms in the terms of the Zernikepolynomial.

In this case, the computer can show image forming quality of theprojection optical system under the reference exposure condition indifferent colors on screen with a permissible value as a boundary, andalso show a screen for setting the weighting. Or, the weighting can beset high in the image forming quality of the projection optical systemunder the reference exposure condition where the image forming qualityexceeds a permissible value.

With the first image forming state adjusting system in the presentinvention, when the information related to image forming quality of theprojection optical system is the information on the difference betweenthe image forming quality of the projection optical system under thereference condition and the predetermined target value of the imageforming quality, and the computer calculates the optimal adjustmentamount using the relation expression, the computer can make the ZernikeSensitivity Chart under the target exposure condition by interpolationcalculation, based on Zernike Sensitivity Charts under a plurality ofreference exposure conditions. In such a case, even in a case where theZernike Sensitivity Chart under the target exposure condition is notprepared in advance, it can be smoothly obtained, for example, byinterpolation calculation using the Zernike Sensitivity Charts under theplurality of reference exposure conditions.

With the first image forming state adjusting system in the presentinvention, the predetermined exposure condition can be the targetexposure condition. In this case, the information related to imageforming quality of the projection optical system can be actualmeasurement data of the image forming quality of the projection opticalsystem under the target exposure condition. In such a case, the computercalculates the optimal adjustment amount under the target exposurecondition based on the adjustment information of the adjustment unit andthe actual measurement data of the image forming quality of theprojection optical system. That is, the optimal adjustment amount of theadjustment unit under the target exposure condition is calculated basedon the actual measurement data of the image forming quality of theprojection optical system measured under the target exposure condition,which allows an accurate calculate of the adjustment amount. In thiscase, the adjustment amount calculated is equally or more accurate,compared with the adjustment amount calculated using the adjustmentinformation of the adjustment unit and the information related to theimage forming quality of the projection optical system under thereference exposure condition referred to earlier.

In this case, as the actual measurement data, any data can be used alongwith the adjustment information of the adjustment unit, as long as itcan be a base for calculating the optimal adjustment amount of theadjustment unit under the target exposure condition. For example, theactual measurement data can include actual measurement data of any imageforming quality under the target exposure condition. Or, the actualmeasurement data can include actual measurement data of wavefrontaberration under the target exposure condition.

With the first image forming state adjusting system in the presentinvention, when the predetermined exposure condition is the targetexposure condition, the information related to image forming quality ofthe projection optical system can be information on a difference betweenthe image forming quality of the projection optical system under thetarget exposure condition and a predetermined target value of the imageforming quality, and the adjustment information of the adjustment unitcan be information on an adjustment amount of the adjustment unit, andin such a case the computer can calculate the optimal adjustment amountusing a relation expression between the difference, a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system under the target exposure condition andcoefficients of each term in a Zernike polynomial, a wavefrontaberration variation table made up of parameters that denotes a relationbetween adjustment of the adjustment unit and a change in wavefrontaberration of the projection optical system, and the adjustment amount.

A predetermined target value of the image forming quality, in this case,includes the case when the target value of the image forming quality(such as aberration) is zero.

In this case, when the target value is not given in particular for thepredetermined target value, it can be set to zero, however, thepredetermined target value can also be a target value of image formingquality in at least one evaluation point of the projection opticalsystem that has been input externally.

In this case, the target value of image forming quality can be a targetvalue of image forming quality at a chosen representative point. Or, thetarget value of image forming quality can be a target value of imageforming quality whose target value of a coefficient is converted, thetarget value of the coefficient being set by decomposing the imageforming quality of the projection optical system into components by anaberration decomposition method and improving a faulty component basedon a decomposition coefficient obtained by the decomposition.

With the first image forming state adjusting system in the presentinvention, when the information related to image forming quality of theprojection optical system is information on a difference between imageforming quality of the projection optical system under the targetexposure condition and a predetermined target value of the image formingquality, and the adjustment information of the adjustment unit isinformation on an adjustment amount of the adjustment unit, the relationexpression used by the computer in order to calculate the optimaladjustment amount can be an equation that includes a weighting functionto perform weighting on any terms in the terms of the Zernikepolynomial.

In this case, the computer can show image forming quality of theprojection optical system under the target exposure condition indifferent colors on screen with a permissible value as a boundary, andalso can show a screen for setting the weighting. Or, the weighting canbe set high in the image forming quality of the projection opticalsystem under the target exposure condition where the image formingquality exceeds a permissible value.

With the first image forming state adjusting system in the presentinvention, when the information related to image forming quality of theprojection optical system is information on a difference between imageforming quality of the projection optical system under the targetexposure condition and a predetermined target value of the image formingquality, the adjustment information of the adjustment unit isinformation on an adjustment amount of the adjustment unit, and thecomputer uses the relation expression to calculate the optimaladjustment amount, the computer can make the Zernike Sensitivity Chartunder the target exposure condition by interpolation calculation, basedon Zernike Sensitivity Charts under a plurality of reference exposureconditions.

With the first image forming state adjusting system in the presentinvention, the computer preferably calculates the optimal adjustmentamount further taking a restraint condition, which is decided by anadjustment amount limit of the adjustment unit, into consideration. Insuch a case, the adjustment unit can be adjusted without fail, accordingto the calculated restraint condition.

With the first image forming state adjusting system in the presentinvention, at least a part of a field of the projection optical systemcan be externally set as an optimizing field range in the computer. Forexample, in the case of a scanning exposure apparatus such as theso-called scanning stepper, there may be a case when the image formingquality or the transferred state of the pattern on the object does nothave to be optimized in the entire field of the projection opticalsystem. Or, in the case of a stepper, depending on the size of the maskthat is used (pattern area), the image forming quality or thetransferred state of the pattern on the object may not have to beoptimized in the entire field of the projection optical system. In suchcases, by externally setting the necessary range as the optimizingfield, the time required for calculating the optimal adjustment amountcan be reduced, compared with when the entire field of the projectionoptical system has been set as the optimizing field.

With the first image forming state adjusting system in the presentinvention, in the computer, from a first mode in which the optimaladjustment amount of the adjustment unit under the target exposurecondition is calculated, based on adjustment information of theadjustment unit and the information related to image forming quality ofthe projection optical system under at least one reference exposurecondition, a second mode in which the optimal adjustment amount of theadjustment unit under the target exposure condition is calculated, basedon actual measurement data of the image forming quality of theprojection optical system under the target exposure condition, and athird mode in which image forming quality of the projection opticalsystem is calculated under an optional exposure condition in a statewhere the adjustment unit has been adjusted according to adjustmentinformation, based on the adjustment information of the adjustment unitand information on wavefront aberration of the projection optical systemunder at least the one reference exposure condition, at least two modescan be set.

In the first image forming state adjusting system in the presentinvention, a worker can perform the adjustment of the adjustment unit bymanual operation, however, the adjustment is not limited to this and thecomputer can control the adjustment unit based on the calculatedadjustment amount.

According to a second aspect of the present invention, there is provideda second image forming state adjusting system used in an exposureapparatus, which forms a projected image of a predetermined pattern onan object using a projection optical system, the system being a systemthat optimizes a forming state of the projected image on the object,comprising: an adjustment unit that adjusts a forming state of theprojected image on the object; and a computer that connects to theexposure apparatus via a communication channel and calculates imageforming quality of the projection optical system under an optionalexposure condition in a state where the adjustment unit has beenadjusted according to adjustment information, based on the adjustmentinformation of the adjustment unit and information on wavefrontaberration of the projection optical system in a state where theadjustment unit has been adjusted according to the adjustmentinformation.

According to this system, the computer that connects to the exposureapparatus via the communication channel calculates the image formingquality of the projection optical system under an optional exposurecondition in a state where the adjustment unit has been adjustedaccording to adjustment information, based on the adjustment informationof the adjustment unit and information on wavefront aberration of theprojection optical system in a state where the adjustment unit has beenadjusted according to the adjustment information. Accordingly, forexample, by making the calculated results of the image forming qualityshow on the computer screen or on the display on the computer sideconnected to the computer, anyone can evaluate on screen whether theimage forming quality of the projection optical system is satisfactoryor not. In addition, with the second image forming state adjustingsystem in the present invention, the best exposure condition can bedecided easily, by calculating and showing the image forming quality,with various exposure conditions set as the target exposure condition.

In this case, the optional exposure condition can be a condition that isdecided according to a first information, which is related to a patternsubject to projection by the projection optical system, and a secondinformation, which is related to projection conditions of the pattern.

In this case, the second information can include numerical aperture ofthe projection optical system and illumination conditions of thepattern.

With the second image forming state adjusting system in the presentinvention, the computer can calculate image forming quality of theprojection optical system under the optional exposure condition based oninformation on the current wavefront aberration of the projectionoptical system, which is obtained based on adjustment information of theadjustment unit and information on wavefront aberration of theprojection optical system under a reference exposure condition, and on aZernike Sensitivity Chart, which denotes a relation between imageforming quality of the projection optical system and coefficients ofeach term in a Zernike polynomial under the optional exposure condition.

With the second image forming state adjusting system in the presentinvention, the computer can make the Zernike Sensitivity Chart under theoptional exposure condition by interpolation calculation, based onZernike Sensitivity Charts under a plurality of reference exposureconditions.

The first and second exposure apparatus in the present invention caneach use a communication channel of various types. For example, thecommunication channel can be a local area network, or it can include apublic line. Or, the communication channel can include a radio link.

In each of the first and second image forming state adjusting systems inthe present invention, the computer can be a computer used forcontrolling that controls each part making up the exposure apparatus.

According to a third aspect of the present invention, there is provideda first exposure method in which a predetermined pattern is transferredonto an object using a projection optical system, the method comprising:a calculating process in which an optimal adjustment amount of anadjustment unit under a target exposure condition is calculated, usingadjustment information of the adjustment unit that adjusts a formingstate of a projected image of the pattern by the projection opticalsystem on the object and information related to image forming quality ofthe projection optical system under a predetermined exposure condition;and a transferring process in which the pattern is transferred onto theobject using the projection optical system, in a state where theadjustment unit has been adjusted based on the calculated adjustmentamount under the target exposure condition.

According to this method, the optimal adjustment amount of theadjustment unit under the target exposure condition is calculated, usingthe adjustment information of the adjustment unit and the informationrelated to image forming quality of the projection optical system undera predetermined exposure condition, that is, under an exposure conditionthat has been decided in advance. That is, because the relation betweenthe adjustment information of the adjustment unit and the informationrelated to image forming quality of the projection optical system(aberration) under a predetermined exposure condition is well known, theoptimal adjustment amount of the image forming quality of the projectionoptical system under the predetermined exposure condition can be easilyfound. Accordingly, the optimal adjustment amount under the targetexposure condition that is calculated using such adjustment informationof the adjustment unit and information related to image forming qualityof the projection optical system under the predetermined exposurecondition is highly precise.

And, in a state where the adjustment unit is adjusted based on thecalculated adjustment amount under the target exposure condition, thepattern is transferred onto the object using the projection opticalsystem. With this method, the forming state of the projected image ofthe pattern on the object is optimally adjusted under any targetexposure condition, and the pattern can be transferred onto the objectwith good precision.

In this case, the information related to image forming quality of theprojection optical system can be information on a difference between theimage forming quality of the projection optical system under thereference exposure condition and a predetermined target value of theimage forming quality, the adjustment information of the adjustment unitcan be information on an adjustment amount of the adjustment unit, andin the calculating process, the optimal adjustment amount can becalculated using a relation expression between the difference, a ZernikeSensitivity Chart that denotes a relation between the image formingquality of the projection optical system and coefficients of each termin a Zernike polynomial under the target exposure condition, a wavefrontaberration variation table made up of parameters that denotes a relationbetween adjustment of the adjustment unit and a change in wavefrontaberration of the projection optical system, and the adjustment amount.

In the first exposure method in the present invention, the predeterminedexposure condition can be the target exposure condition.

In this case, the information related to image forming quality of theprojection optical system can be actual measurement data of the imageforming quality of the projection optical system under the targetexposure condition.

In this case, the actual measurement data can include actual measurementdata of wavefront aberration under the target exposure condition.

In the first exposure method in the present invention, when thepredetermined exposure condition is the target exposure condition, theinformation related to image forming quality of the projection opticalsystem can be information on a difference between the image formingquality of the projection optical system under the target exposurecondition and a predetermined target value of the image forming quality,the adjustment information of the adjustment unit can be information onan adjustment amount of the adjustment unit, and in the calculatingprocess, the optimal adjustment amount can be calculated using arelation expression between the difference, a Zernike Sensitivity Chartthat denotes a relation between image forming quality of the projectionoptical system and coefficients of each term in a Zernike polynomialunder the target exposure condition, a wavefront aberration variationtable made up of parameters that denotes a relation between adjustmentof the adjustment unit and a change in wavefront aberration of theprojection optical system, and the adjustment amount.

In the first exposure method in the present invention, the relationexpression used for calculating the optimal adjustment amount can be anequation that includes a weighting function to perform weighting on anyterms in the terms of the Zernike polynomial.

According to a fourth aspect of the present invention, there is provideda second exposure method in which a pattern is transferred onto anobject via a projection optical system, the method comprising:calculating image forming quality of the projection optical system undera plurality of exposure conditions that have different setting values,which are related to setting information being focused on among aplurality of setting information for the transfer, respectively, basedon information related to wavefront aberration of the projection opticalsystem and a Zernike Sensitivity Chart that denotes a relation betweenthe image forming quality of the projection optical system andcoefficients of each term in a Zernike polynomial; and deciding anexposure condition whose setting values related to the settinginformation being focused on are optimal, based on the image formingquality calculated for each of the exposure conditions.

According to this method, the image forming quality of the projectionoptical system is calculated under a plurality of exposure conditionsthat have different setting values, which are related to settinginformation being focused on among a plurality of setting informationfor the transfer, respectively, based on information related towavefront aberration of the projection optical system and a ZernikeSensitivity Chart that denotes a relation between the image formingquality of the projection optical system and coefficients of each termin a Zernike polynomial, and the exposure condition whose setting valuesrelated to the setting information being focused on are optimal isdecided, based on the image forming quality calculated for each of theexposure conditions. Accordingly, the best exposure condition can beeasily set for each setting information, or for any number or types ofsetting information, using setting values that makes the image formingquality optimal, and the pattern can be transferred onto the object viathe projection optical system with good precision.

In this case, when the plurality of setting information includeinformation related to a pattern subject to projection by the projectionoptical system, an optimal setting value can be decided with theinformation related to a pattern serving as the setting informationbeing focused on.

In the second exposure method in the present invention, when theplurality of setting information include a plurality of informationrelated to projection conditions of a pattern subject to projection bythe projection optical system, an optimal setting value can be decidedwith the one of the plurality of information related to projectionconditions serving as the setting information being focused on.

In this case, the plurality of information related to projectionconditions can include optical information of the projection opticalsystem and that of an illumination optical system illuminating thepattern.

In this case, the optical information of the illumination optical systemcan include a plurality of information related to illuminationconditions of the pattern.

In the second exposure method in the present invention, the imageforming quality can be calculated, each by using a Zernike SensitivityChart that is different in at least a part of the plurality of exposureconditions.

In this case, at least one of the plurality of exposure conditions canhave its corresponding Zernike Sensitivity Chart made by interpolationcalculation, based on Zernike Sensitivity Charts corresponding to otherexposure conditions in the plurality of exposure conditions.

In the second exposure method in the present invention, an optimaladjustment amount of the adjustment unit can be decided under anexposure condition whose setting values related to the settinginformation being focused on is optimal, based on a wavefront aberrationvariation table that denotes a relation between adjustment of a formingstate of a projected image of the pattern by the projection opticalsystem on the object by the adjustment unit and a change in wavefrontaberration of the projection optical system, and the Zernike SensitivityChart.

In this case, when the pattern is transferred onto the object under theexposure condition whose setting values related to the settinginformation being focused on is optimal, at least one optical element ofthe projection optical system can be adjusted according to the optimaladjustment amount. Or, the optimal adjustment amount can be calculatedusing a weighting function that performs weighting on at least one termof the Zernike polynomial. Or, the image forming quality can becalculated, each by using a Zernike Sensitivity Chart that is differentin at least a part of the plurality of exposure conditions. In thiscase, at least one of the plurality of exposure conditions can have itscorresponding Zernike Sensitivity Chart made by interpolationcalculation, based on Zernike Sensitivity Charts corresponding to otherexposure conditions in the plurality of exposure conditions.

According to a fifth aspect of the present invention, there is provideda third exposure method in which a pattern is transferred onto an objectvia a projection optical system wherein an optimal adjustment amount ofan adjustment unit under an exposure condition whose image formingquality of the projection optical system is optimal is decided, based oninformation related to wavefront aberration of the projection opticalsystem, a Zernike Sensitivity Chart that denotes a relation between theimage forming quality of the projection optical system and coefficientsof each term in a Zernike polynomial, and a wavefront aberrationvariation table that denotes a relation between adjustment by theadjustment unit of a forming state of a pattern image via the projectionoptical system on the object and a change in wavefront aberration of theprojection optical system.

According to this method, the optimal adjustment amount of an adjustmentunit under an exposure condition whose image forming quality of theprojection optical system is optimal is decided, based on informationrelated to wavefront aberration of the projection optical system, aZernike Sensitivity Chart that denotes a relation between the imageforming quality of the projection optical system and coefficients ofeach term in a Zernike polynomial, and a wavefront aberration variationtable that denotes a relation between adjustment by the adjustment unitof a forming state of a pattern image via the projection optical systemon the object and a change in wavefront aberration of the projectionoptical system. Therefore, the optimal adjustment amount of theadjustment unit under the exposure condition whose the image formingquality is optimal can be set according to the information related tothe known wavefront aberration of the projection optical system andinformation related to the pattern, and by adjusting the adjustment unitusing the decided adjustment value and performing exposure, the patterncan be transferred onto the object via the projection optical systemwith good precision.

In this case, when the pattern is transferred onto the object under theexposure condition whose image forming quality is optimal, at least oneoptical element of the projection optical system can be adjustedaccording to the optimal adjustment amount. Or, the optimal adjustmentamount can be calculated using a weighting function that performsweighting on at least one term of the Zernike polynomial.

In the third exposure method in the present invention, the optimaladjustment amount of the adjustment unit that makes image formingquality of the projection optical system optimal can be decided undereach of a plurality of exposure conditions that have a different settingvalue in at least one setting information among a plurality of settinginformation for the transfer.

In this case, the optimal adjustment amount can be calculated, each byusing a Zernike Sensitivity Chart that is different in at least a partof the plurality of exposure conditions.

In this case, at least one of the plurality of exposure conditions canhave its corresponding Zernike Sensitivity Chart made by interpolationcalculation, based on Zernike Sensitivity Charts corresponding to otherexposure conditions in the plurality of exposure conditions. Or, whenthe plurality of setting information include information related to apattern subject to projection by the projection optical system, theoptimal adjustment amount of the adjustment unit that makes imageforming quality of the projection optical system optimal can be decidedunder each of a plurality of exposure conditions whose the pattern isdifferent.

Or, the plurality of setting information can include projectioninformation related to projection conditions of a pattern subject toprojection by the projection optical system, and the optimal adjustmentamount of the adjustment unit that makes image forming quality of theprojection optical system optimal can be decided under each of aplurality of exposure conditions whose setting values related to theprojection information are different.

In this case, the information related to the projection conditions caninclude optical information of the projection optical system and that ofan illumination optical system that illuminates the pattern, and theoptimal adjustment amount of the adjustment unit that makes imageforming quality of the projection optical system optimal can be decidedunder each of a plurality of exposure conditions whose setting valuesrelated to at least one of the two optical information of the projectionoptical system are different.

In this case, the optical information of the illumination optical systemcan include a plurality of illumination information related toillumination conditions of the pattern, and the optimal adjustmentamount of the adjustment unit that makes image forming quality of theprojection optical system optimal can be decided under each of aplurality of exposure conditions whose setting values related to atleast one illumination information in the plurality of illuminationinformation are different.

According to a sixth aspect of the present invention, there is provideda first exposure apparatus that transfers a pattern on an object via aprojection optical system, the apparatus comprising: a setting unit thatsets an exposure condition whose setting values are variable in at leastone setting information among a plurality of setting information relatedto projection conditions of a pattern subject to projection by theprojection optical system; and a calculating unit that calculates imageforming quality of the projection optical system under a plurality ofexposure conditions that have different setting values, which arerelated to setting information being focused on among a plurality ofsetting information, respectively, based on information related towavefront aberration of the projection optical system and a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system and coefficients of each term in aZernike polynomial, and decides an exposure condition whose settingvalues related to the setting information being focused on are optimal,based on the image forming quality calculated for each of the exposureconditions.

With this apparatus, the setting unit sets an exposure condition whosesetting values are variable in at least one setting information among aplurality of setting information related to projection conditions of apattern subject to projection by the projection optical system. And, thecalculating unit calculates image forming quality of the projectionoptical system under a plurality of exposure conditions that havedifferent setting values, which are related to setting information beingfocused on among a plurality of setting information, respectively, basedon information related to wavefront aberration of the projection opticalsystem and a Zernike Sensitivity Chart that denotes a relation betweenimage forming quality of the projection optical system and coefficientsof each term in a Zernike polynomial, and decides the exposure conditionwhose setting values related to the setting information being focused onare optimal, based on the image forming quality calculated for each ofthe exposure conditions. Accordingly, the best exposure condition can beeasily set for each setting information, or for any number or types ofsetting information, using setting values that makes the image formingquality optimal, and the pattern can be transferred onto the object viathe projection optical system with good precision.

In this case, the image forming quality can be calculated, each by usinga Zernike Sensitivity Chart that is different in at least a part of theplurality of exposure conditions.

In this case, at least one of the plurality of exposure conditions canhave its corresponding Zernike Sensitivity Chart made by interpolationcalculation, based on Zernike Sensitivity Charts corresponding to otherexposure conditions in the plurality of exposure conditions.

With the first exposure apparatus in the present invention, the exposureapparatus can further comprise: an adjustment unit that adjusts aforming state of a projected image on the object by the projectionoptical system, wherein the exposure apparatus can decide an optimaladjustment amount of the adjustment unit under an exposure conditionwhose setting values related to the setting information being focused onare optimal, based on a wavefront aberration variation table thatdenotes a relation between adjustment by the adjustment unit and achange in wavefront aberration of the projection optical system, and theZernike Sensitivity Chart.

In this case, when the pattern is transferred onto the object under theexposure condition whose setting values related to the settinginformation being focused on is optimal, at least one optical element ofthe projection optical system can be adjusted according to the optimaladjustment amount. Or, the optimal adjustment amount can be calculatedusing a weighting function that performs weighting on at least one termof the Zernike polynomial.

According to a seventh aspect of the present invention, there isprovided a second exposure apparatus that transfers a pattern on anobject via a projection optical system, the apparatus comprising: anadjustment unit that adjusts a forming state of a pattern image by theprojection optical system on the object; a calculating unit that decidesan optimal adjustment amount of the adjustment unit under an exposurecondition whose image forming quality of the projection optical systemis optimal, based on information related to wavefront aberration of theprojection optical system, a Zernike Sensitivity Chart that denotes arelation between image forming quality of the projection optical systemand coefficients of each term in a Zernike polynomial, and a wavefrontaberration variation table that denotes a relation between adjustment bythe adjustment unit and a change in wavefront aberration of theprojection optical system.

With this apparatus, the calculating unit calculates the opticaladjustment amount of the adjustment unit under an exposure conditionwhose image forming quality of the projection optical system is optimal,based on information related to wavefront aberration of the projectionoptical system, a Zernike Sensitivity Chart that denotes a relationbetween the image forming quality of the projection optical system andcoefficients of each term in a Zernike polynomial, and a wavefrontaberration variation table that denotes a relation between adjustment bythe adjustment unit and a change in wavefront aberration of theprojection optical system. Therefore, by providing the informationrelated to wavefront aberration of the projection optical system and theinformation related to the pattern, the calculating unit decides theoptimal adjustment amount of the adjustment unit under the exposurecondition whose image forming quality of the projection optical systemis optimal. Then, by performing exposure in a state where the adjustmentunit is adjusted using the adjustment amount that has been decided, thepattern can be transferred onto the object with good accuracy via theprojection optical system.

In this case, the optimal adjustment amount can be calculated using aweighting function that performs weighting on at least one term of theZernike polynomial.

With the second exposure apparatus in the present invention, the optimaladjustment amount of the adjustment unit that makes image formingquality of the projection optical system optimal can be decided undereach of a plurality of exposure conditions that have a different settingvalue in at least one setting information among a plurality of settinginformation for the transfer.

In this case, the optimal adjustment amount can be decided, each byusing a Zernike Sensitivity Chart that is different in at least a partof the plurality of exposure conditions.

In this case, at least one of the plurality of exposure conditions canhave its corresponding Zernike Sensitivity Chart made by interpolationcalculation, based on Zernike Sensitivity Charts corresponding to otherexposure conditions in the plurality of exposure conditions.

According to an eighth aspect of the present invention, there isprovided a third exposure apparatus that transfers a pattern on anobject via a projection optical system, the apparatus comprising: asetting unit that sets an exposure condition whose setting values arevariable in at least one setting information among a plurality ofsetting information related to projection conditions of a patternsubject to projection by the projection optical system; and acalculating unit that uses a Zernike Sensitivity Chart, which isdifferent in at least a part of a plurality of exposure conditions, andalso makes at least one Zernike Sensitivity Chart different in at leasta part of the plurality of exposure conditions by interpolationcalculation based on a plurality of other Zernike Sensitivity Charts, oncalculating image forming quality of the projection optical system undera plurality of exposure conditions that have different setting values,which are related to setting information being focused on among aplurality of setting information, respectively, based on informationrelated to wavefront aberration of the projection optical system and aZernike Sensitivity Chart that denotes a relation between image formingquality of the projection optical system and coefficients of each termin a Zernike polynomial.

With this apparatus, the setting unit sets an exposure condition whosesetting values are variable in at least one setting information among aplurality of setting information related to projection conditions of apattern subject to projection by the projection optical system. And, thecalculating unit uses a Zernike Sensitivity Chart, which is different inat least a part of a plurality of exposure conditions, and also makes atleast one Zernike Sensitivity Chart different in at least a part of theplurality of exposure conditions by interpolation calculation based on aplurality of other Zernike Sensitivity Charts, on calculating imageforming quality of the projection optical system under a plurality ofexposure conditions that have different setting values, which arerelated to setting information being focused on among a plurality ofsetting information, respectively, based on information related towavefront aberration of the projection optical system and a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system and coefficients of each term in aZernike polynomial. Accordingly, even when the Zernike Sensitivity Chartis not prepared in advance under each of a plurality of exposureconditions, the Zernike Sensitivity Chart under the target exposurecondition can be obtained by interpolation calculation based on aplurality of other Zernike Sensitivity Charts.

According to a ninth aspect of the present invention, there is provideda fourth exposure method in which a pattern is transferred onto anobject via a projection optical system wherein a Zernike SensitivityChart, which is different in at least a part of a plurality of exposureconditions, is used, and also at least one Zernike Sensitivity Chartdifferent in at least a part of the plurality of exposure conditions ismade by interpolation calculation based on a plurality of other ZernikeSensitivity Charts, on calculating image forming quality of theprojection optical system under a plurality of exposure conditions thathave different setting values, which are related to setting informationbeing focused on among a plurality of setting information related toprojection conditions of a pattern subject to projection by theprojection optical system, respectively, based on information related towavefront aberration of the projection optical system and a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system and coefficients of each term in aZernike polynomial.

According to this method, even when the Zernike Sensitivity Chart is notprepared in advance under each of a plurality of exposure conditions,the Zernike Sensitivity Chart under the target exposure condition can beobtained by interpolation calculation based on a plurality of otherZernike Sensitivity Charts.

According to a tenth aspect of the present invention, there is provideda fourth exposure apparatus that irradiates an energy beam on a mask andtransfers a pattern formed on the mask onto an object via a projectionoptical system, the apparatus comprising: an adjustment unit thatadjusts a forming state of a projected image of the pattern on theobject; and a processing unit that connects to the adjustment unit via asignal cable and calculates an optimal adjustment amount of theadjustment unit under a target exposure condition, based on adjustmentinformation of the adjustment unit and information related to imageforming quality of the projection optical system under a predeterminedexposure condition, and controls the adjustment unit based on thecalculated adjustment amount.

With this apparatus, the processing unit calculates the optimaladjustment amount of the adjustment unit under a target exposurecondition, based on adjustment information of the adjustment unit andinformation related to image forming quality of the projection opticalsystem under a predetermined exposure condition, and controls theadjustment unit based on the calculated adjustment amount. As ispreviously described, the relation between the adjustment information ofthe adjustment unit and the information related to image forming qualityof the projection optical system (aberration) under a predeterminedexposure condition is well known, therefore, the optimal adjustmentamount that makes the image forming quality of the projection opticalsystem optimal under the predetermined exposure condition can be easilyfound. Accordingly, the optimal adjustment amount under the targetexposure condition that is calculated using the adjustment informationof the adjustment unit and the information related to image formingquality of the projection optical system under a predetermined exposurecondition is highly precise, and because the adjustment unit is adjustedbased on the adjustment amount, the forming state of the projected imageof the pattern on the object under any target exposure condition issubstantially automatically optimized.

In this case, the predetermined exposure condition can be at least onereference exposure condition. In such a case, at least one referenceexposure condition can be set as the predetermined exposure condition,in which the adjustment amount for optimally adjusting the image formingquality of the projection optical system is obtained in advance, and theoptimal adjustment amount under the target exposure condition that iscalculated based on the adjustment information of the adjustment unitand the information related to the image forming quality of theprojection optical system under such reference exposure condition willhave high precision.

In this case, the information related to image forming quality caninclude various types of information, so long as it is information thatcan be a base on calculating the optimal adjustment amount of theadjustment unit under the target exposure condition, along with theadjustment information of the adjustment unit. For example, theinformation related to image forming quality can include information onwavefront aberration of the projection optical system that has beenadjusted under the reference exposure condition. Or, the informationrelated to image forming quality can include information on astand-alone wavefront aberration of the projection optical system andimage forming quality of the projection optical system under thereference exposure condition.

With the fourth exposure apparatus in the present invention, when thepredetermined exposure condition is an exposure condition that serves asat least one reference, the information related to image forming qualityof the projection optical system can be information on a differencebetween image forming quality of the projection optical system under thereference exposure condition and a predetermined target value of theimage forming quality, the adjustment information of the adjustment unitcan be information on an adjustment amount of the adjustment unit, andthe processing unit can calculate the optimal adjustment amount using arelation expression between the difference, a Zernike Sensitivity Chartthat denotes a relation between image forming quality of the projectionoptical system and coefficients of each term in a Zernike polynomialunder the target exposure condition, a wavefront aberration variationtable made up of parameters that denotes a relation between adjustmentof the adjustment unit and a change in wavefront aberration of theprojection optical system, and the adjustment amount.

With the fourth exposure apparatus in the present invention, thepredetermined exposure condition can be the target exposure condition.In this case, the information related to image forming quality of theprojection optical system can be actual measurement data of the imageforming quality of the projection optical system under the targetexposure condition. In such a case, the processing unit calculates theoptimal adjustment amount of the adjustment unit under the targetexposure condition, based on adjustment information of the adjustmentunit and actual measurement data of the image forming quality of theprojection optical system under the target exposure condition, andcontrols the adjustment unit based on the calculated adjustment amount.In this case, because the optimal adjustment amount of the adjustmentunit under the target exposure condition is decided based on actualmeasurement data of the image forming quality of the projection opticalsystem measured under the target exposure condition, the adjustmentamount can be accurately calculated, and, since the adjustment unit isadjusted based on such adjustment amount, the forming state of theprojected image of the pattern on the object under any target exposurecondition can be substantially optimized automatically. The adjustmentamount calculated in this case, is equal or more accurate, compared withthe adjustment amount calculated using adjustment information of theadjustment unit and information related to image forming quality underthe reference exposure condition, previously described.

In this case, as the actual measurement data, any data can be used aslong as it can be a base for calculating the optimal adjustment amountof the adjustment unit under the target exposure condition, along withthe adjustment information of the adjustment unit. For example, theactual measurement data can include actual measurement data of anoptional image forming quality under the target exposure condition, or,the actual measurement data can include actual measurement data ofwavefront aberration under the target exposure condition. In the lattercase, the apparatus can further comprise a wavefront measuringinstrument that measures wavefront aberration of the projection opticalsystem.

In this case, the apparatus can further comprise: an object stage thatholds the object; and a carriage system that loads and unloads thewavefront measuring instrument to the object stage.

With the fourth exposure apparatus in the present invention, when thepredetermined exposure condition is the target exposure condition, theinformation related to image forming quality of the projection opticalsystem can be information on a difference between image forming qualityof the projection optical system under the target exposure condition anda predetermined target value of the image forming quality, theadjustment information of the adjustment unit can be information on anadjustment amount of the adjustment unit, and the processing unit cancalculate the optimal adjustment amount using a relation expressionbetween the difference, a Zernike Sensitivity Chart that denotes arelation between image forming quality of the projection optical systemand coefficients of each term in a Zernike polynomial under the targetexposure condition, a wavefront aberration variation table made up ofparameters that denotes a relation between adjustment of the adjustmentunit and a change in wavefront aberration of the projection opticalsystem, and the adjustment amount.

With the fourth exposure apparatus in the present invention, when theprocessing unit calculates the optimal adjustment amount using therelation expression, the predetermined target value can be a targetvalue of image forming quality in at least one evaluation point of theprojection optical system that has been input externally.

The target value of image forming quality can be a target value of imageforming quality at a chosen representative point, or, the target valueof image forming quality can be a target value of image forming qualitywhose target value of a coefficient is converted, the target value ofthe coefficient being set by decomposing the image forming quality ofthe projection optical system into components by an aberrationdecomposition method and improving a faulty component based on adecomposition coefficient obtained by the decomposition.

With the fourth exposure apparatus in the present invention, when theprocessing unit calculates the optimal adjustment amount using therelation expression, the relation expression can be an equation thatincludes a weighting function to perform weighting on any terms in theterms of the Zernike polynomial.

In this case, the processing unit can show image forming quality of theprojection optical system under the predetermined exposure condition indifferent colors on screen with a permissible value as a boundary, andalso can show a screen for setting the weighting.

With the fourth exposure apparatus in the present invention, when theprocessing unit calculates the optimal adjustment amount using therelation expression, the processing unit can make the ZernikeSensitivity Chart under the target exposure condition by interpolationcalculation, based on Zernike Sensitivity Charts under a plurality ofreference exposure conditions.

According to an eleventh aspect of the present invention, there isprovided a fifth exposure apparatus that irradiates an energy beam on amask and transfers a pattern formed on the mask onto an object via aprojection optical system, the apparatus comprising: an adjustment unitthat adjusts a forming state of a projected image on the object; and aprocessing unit that connects to the adjustment unit via a communicationchannel and calculates image forming quality of the projection opticalsystem under an optional exposure condition in a state where theadjustment unit is adjusted according to adjustment information, basedon the adjustment information of the adjustment unit and information onwavefront aberration of the projection optical system in a state wherethe adjustment unit is adjusted according to the adjustment information.

With this apparatus, the processing unit that connects to the adjustmentunit via the communication channel calculates image forming quality ofthe projection optical system under an optional exposure condition in astate where the adjustment unit is adjusted according to adjustmentinformation, based on the adjustment information of the adjustment unitand information on wavefront aberration of the projection optical systemin a state where the adjustment unit is adjusted according to theadjustment information. Accordingly, for example, by making thecalculated results of the image forming quality show on the computerscreen or on the display on the computer side connected to the computer,anyone can evaluate on screen whether the image forming quality of theprojection optical system is satisfactory or not. In addition, with thefifth exposure apparatus in the present invention, the best exposurecondition can be decided easily, by calculating and showing the imageforming quality, with various exposure conditions set as the targetexposure condition.

In this case, the optional exposure condition can be a condition that isdecided according to a first information, which is related to a patternsubject to projection by the projection optical system, and a secondinformation, which is related to projection conditions of the pattern.

In this case, the second information can include numerical aperture ofthe projection optical system and illumination conditions of thepattern.

With the fifth exposure apparatus in the present invention, theprocessing unit can calculate image forming quality of the projectionoptical system under the optional exposure condition based oninformation on the current wavefront aberration of the projectionoptical system, which is obtained based on adjustment information of theadjustment unit and information on wavefront aberration of theprojection optical system under a reference exposure condition, and on aZernike Sensitivity Chart, which denotes a relation between imageforming quality of the projection optical system and coefficients ofeach term in a Zernike polynomial under the optional exposure condition.

In this case, the processing unit can make the Zernike Sensitivity Chartunder the optional exposure condition by interpolation calculation,based on Zernike Sensitivity Charts under a plurality of referenceexposure conditions.

According to a twelfth aspect of the present invention, there isprovided a first program that makes a computer, which makes up a part ofa control system of an exposure apparatus that forms a projected imageof a predetermined pattern on an object using a projection opticalsystem and also comprises an adjustment unit to adjust a forming stateof the projected image on the object, execute a predetermined process,the program making the computer execute a procedure of: calculating anoptimal adjustment amount of the adjustment unit under a target exposurecondition in response to input of adjustment information of theadjustment unit and information related to image forming quality of theprojection optical system under a predetermined exposure condition,using the input information.

When the target exposure condition, and adjustment information on theadjustment unit and information related to image forming quality of theprojection optical system are input into a computer that has the programinstalled, the computer calculates the optimal adjustment amount of theadjustment unit under the target exposure condition in response, usingthe input information. That is, the relation between adjustmentinformation on the adjustment unit and information related to imageforming quality of the projection optical system (aberration) under thepredetermined exposure condition is well known, therefore, the optimaladjustment amount of the image forming quality of the projection opticalsystem under the predetermined exposure condition can be easily found.Accordingly, the optimal adjustment amount under the target exposurecondition that is calculated based on adjustment information of theadjustment unit and information related to image forming quality of theprojection optical system under such predetermined exposure condition ishighly precise. Therefore, by adjusting the adjustment unit based on theadjustment amount, the forming state of the projected image of thepattern on the object under any target exposure condition can besmoothly optimized. As is described, the first program in the presentinvention makes the computer execute a process of smoothly optimizingthe image forming state of the pattern by the projection optical system,or to be more precise, makes the computer calculate the optimaladjustment amount under the target exposure condition.

In this case, the predetermined exposure condition can be at least onereference exposure condition. In such a case, at least one referenceexposure condition whose optimal adjustment amount of the projectionoptical system is obtained in advance can be set as the predeterminedexposure condition, and the optimal adjustment amount under the targetexposure condition calculated based on adjustment information of theadjustment unit and information related to image forming quality of theprojection optical system under such reference exposure condition ishighly precise.

In this case, the information related to image forming quality only hasto be information that can be a base for calculating the optimaladjustment amount of the adjustment unit under the target exposurecondition, along with the adjustment information of the adjustment unit,and for example, the information related to image forming quality caninclude information on wavefront aberration of the projection opticalsystem that has been adjusted under the reference exposure condition.Or, the information related to image forming quality can includeinformation on a stand-alone wavefront aberration of the projectionoptical system and image forming quality of the projection opticalsystem under the reference exposure condition.

In the first program of the present invention, when the predeterminedexposure condition is at least one reference exposure condition, theinformation related to image forming quality of the projection opticalsystem can be information on a difference between image forming qualityof the projection optical system under the reference exposure conditionand a predetermined target value of the image forming quality, theadjustment information of the adjustment unit can be information on anadjustment amount of the adjustment unit, and the program can make thecomputer calculate the optimal adjustment amount using a relationexpression between the difference, a Zernike Sensitivity Chart thatdenotes a relation between image forming quality of the projectionoptical system and coefficients of each term in a Zernike polynomialunder the target exposure condition, a wavefront aberration variationtable made up of parameters that denotes a relation between adjustmentof the adjustment unit and a change in wavefront aberration of theprojection optical system, and the adjustment amount.

In this case, the program can further make the computer execute aprocedure of: showing a setting screen of the target value at eachevaluation point within a field of the projection optical system. Insuch a case, the predetermined target vale can be a target value ofimage forming quality in at least one representative point set inresponse to the above showing of the setting screen.

In the first program in the present invention, when the informationrelated to image forming quality of the projection optical system isinformation on a difference between image forming quality of theprojection optical system under the reference exposure condition and apredetermined target value of the image forming quality, and theadjustment information of the adjustment unit is information on anadjustment amount of the adjustment unit, and the program makes thecomputer calculate the optimal adjustment amount using the relationexpression, the program can further make the computer execute aprocedure of: decomposing image forming quality of the projectionoptical system into components by an aberration the method and showing asetting screen of a target value along with the coefficients obtained bythe decomposing; and converting the target value of a coefficient set inresponse to showing the setting screen into a target value of the imageforming quality. In addition, in this case, the relation expression canbe an equation that includes a weighting function to perform weightingon any terms in the terms of the Zernike polynomial.

In this case, the program can further make the computer execute aprocedure of: showing image forming quality of the projection opticalsystem under the reference exposure condition in different colors onscreen with a permissible value of a boundary, and also shows a screenfor setting the weighting.

In the first program in the present invention, when the predeterminedexposure condition is at least one reference exposure condition, and theprogram makes the computer calculate the optimal adjustment amount usingthe relation expression, the program can further make the computerexecute a procedure of: making the Zernike Sensitivity Chart under thetarget exposure condition by interpolation calculation, based on ZernikeSensitivity Charts under a plurality of reference exposure conditions.

In the first program in the present invention, when the predeterminedexposure condition is at least one reference exposure condition, theprogram can further make the computer execute a procedure of: correctingthe optimal adjustment amount taking a restraint condition, which isdecided by an adjustment amount limit of the adjustment unit, intoconsideration.

In the first program in the present invention, the predeterminedexposure condition can be the target exposure condition. In this case,the information related to image forming quality of the projectionoptical system can be actual measurement data of image forming qualityof the projection optical system under the target exposure condition. Insuch a case, when adjustment information on the adjustment unit and theactual measurement data of image forming quality of the projectionoptical system under the target exposure condition are input into thecomputer, the computer calculates the optimal adjustment amount of theadjustment unit under the target exposure condition in response, usingthe input information. That is, because the optimal adjustment amount ofthe adjustment unit under the target exposure condition is calculated,based on the actual measurement data of image forming quality of theprojection optical system measured under the target exposure condition,the adjustment amount can be accurately calculated. Therefore, byadjusting the adjustment unit based on the adjustment amount, theforming state of the projected image of the pattern on the object underany target exposure condition can be smoothly optimized. In this case,the calculated adjustment amount will be equally or more precise whencompared with the adjustment amount calculated using adjustmentinformation of the adjustment unit and information related to imageforming quality of the projection optical system.

In this case, as the actual measurement data, any kind of data may beused, as long as it can be a base for calculating the optimal adjustmentamount of the adjustment unit under the target exposure condition, alongwith the adjustment information of the adjustment unit. For example, theactual measurement data can include actual measurement data of anoptional image forming quality under the target exposure condition. Or,the actual measurement data can include actual measurement data ofwavefront aberration under the target exposure condition.

In the first program in the present invention, when the predeterminedexposure condition is the target exposure condition, the informationrelated to image forming quality of the projection optical system can beinformation on a difference between image forming quality of theprojection optical system under the target exposure condition and apredetermined target value of the image forming quality, the adjustmentinformation of the adjustment unit can be information on an adjustmentamount of the adjustment unit, and the program can make the computercalculate the optimal adjustment amount using a relation expressionbetween the difference, a Zernike Sensitivity Chart that denotes arelation between image forming quality of the projection optical systemand coefficients of each term in a Zernike polynomial under the targetexposure condition, a wavefront aberration variation table made up ofparameters that denotes a relation between adjustment of the adjustmentunit and a change in wavefront aberration of the projection opticalsystem, and the adjustment amount.

In this case, the program can further make the computer execute aprocedure of: showing a setting screen of the target value at eachevaluation point within a field of the projection optical system. Insuch a case, the predetermined target vale can be a target value ofimage forming quality in at least one representative point set inresponse to the above showing of the setting screen.

In the first program in the present invention, when the informationrelated to image forming quality of the projection optical system isinformation on a difference between image forming quality of theprojection optical system under the target exposure condition and apredetermined target value of the image forming quality, and theadjustment information of the adjustment unit is information on anadjustment amount of the adjustment unit, and the program makes thecomputer calculate the optimal adjustment amount using the relationexpression, the program can make the computer calculate the optimaladjustment amount using the relation expression that denotes therelation between the difference, a Zernike Sensitivity Chart thatdenotes a relation between image forming quality of the projectionoptical system and coefficients of each term in a Zernike polynomialunder the target exposure condition, a wavefront aberration variationtable made up of parameters that denotes a relation between adjustmentof the adjustment unit and a change in wavefront aberration of theprojection optical system, and the adjustment amount. In addition, inthis case, the relation expression can be an equation that includes aweighting function to perform weighting on any terms in the terms of theZernike polynomial.

In this case, the program can further make the computer execute aprocedure of: showing image forming quality of the projection opticalsystem under the target exposure condition in different colors on screenwith a permissible value as a boundary, and also shows a screen forsetting the weighting.

In the first program in the present invention, when the predeterminedexposure condition is the target exposure condition and the programmakes the computer calculate the optimal adjustment amount using therelation expression, the program can further make the computer execute aprocedure of: making the Zernike Sensitivity Chart under the targetexposure condition by interpolation calculation, based on ZernikeSensitivity Charts under a plurality of reference exposure conditions.

In the first program in the present invention, when the predeterminedexposure condition is the target exposure condition, the program canfurther make the computer execute a procedure of: correcting the optimaladjustment amount taking a restraint condition, which is decided by anadjustment amount limit of the adjustment unit, into consideration.

In the first program in the present invention, the program can furthermake the computer execute a procedure of: selectively setting a mode inresponse to mode selection instructions for at least two modes out ofmodes set in advance, the modes being a first mode in which the optimaladjustment amount of the adjustment unit under the target exposurecondition is calculated, based on adjustment information of theadjustment unit and the information related to image forming quality ofthe projection optical system under at least one reference exposurecondition, a second mode in which the optimal adjustment amount of theadjustment unit under the target exposure condition is calculated, basedon actual measurement data of image forming quality of the projectionoptical system under the target exposure condition, and a third mode inwhich image forming quality of the projection optical system iscalculated under an optional exposure condition in a state where theadjustment unit has been adjusted according to adjustment information,based on the adjustment information of the adjustment unit andinformation on wavefront aberration of the projection optical systemunder at least the one reference exposure condition.

In the first program in the present invention, the program can furthermake the computer execute a procedure of: controlling the adjustmentunit based on the calculated adjustment amount.

According to a thirteenth aspect of the present invention, there isprovided a second program that makes a computer, which makes up a partof a control system of an exposure apparatus that forms a projectedimage of a predetermined pattern on an object using a projection opticalsystem and also comprises an adjustment unit to adjust a forming stateof the projected image on the object, execute a predetermined process,the program making the computer execute a procedure of: calculatingimage forming quality of the projection optical system under an optionalexposure condition in a state where the adjustment unit has beenadjusted according to adjustment information using the adjustmentinformation of the adjustment unit and information on wavefrontaberration of the projection optical system under at least one referenceexposure condition; and outputting results of the calculation.

When adjustment information on the adjustment unit and information onwavefront aberration of the projection optical system under at least onereference exposure condition are input into the computer that has theprogram installed, the computer calculates the image forming quality ofthe projection optical system under an optional exposure condition in astate where the adjustment unit has been adjusted according to theadjustment information in response, using the input information, andshows the calculation results on screen. Accordingly, anyone can easilyevaluate on screen whether the image forming quality of the projectionoptical system is satisfactory or not, based on the calculation resultsof the output image forming quality. In addition, in the second programin the present invention, by inputting various exposure conditions asthe target exposure condition and making the computer output thecalculation results of image forming quality, the best exposurecondition can be easily decided.

In this case, the optional exposure condition can be a condition that isdecided according to a first information, which is related to a patternsubject to projection by the projection optical system, and a secondinformation, which is related to projection conditions of the pattern.

In this case, the second information can include numerical aperture ofthe projection optical system and illumination conditions of thepattern.

In the second program in the present invention, the program can make thecomputer calculate image forming quality of the projection opticalsystem under the optional exposure condition based on information on thecurrent wavefront aberration of the projection optical system, which isobtained based on adjustment information of the adjustment unit andinformation on wavefront aberration of the projection optical systemunder a reference exposure condition, and on a Zernike SensitivityChart, which denotes a relation between image forming quality of theprojection optical system and coefficients of each term in a Zernikepolynomial under the optional exposure condition.

In the second program in the present invention, the program can furthermake the computer execute a procedure of: making the Zernike SensitivityChart under the optional exposure condition by interpolationcalculation, based on Zernike Sensitivity Charts under a plurality ofreference exposure conditions.

According to a fourteenth aspect of the present invention, there isprovided a third program of a computer that makes an exposure apparatus,which transfers a pattern onto an object via a projection opticalsystem, execute a predetermined process, the program making the computerexecute a procedure of: calculating image forming quality of theprojection optical system under a plurality of exposure conditions thathave different setting values, which are related to setting informationbeing focused on among a plurality of setting information for thetransfer, respectively, in response to input of information related towavefront aberration of the projection optical system and a ZernikeSensitivity Chart that denotes a relation between image forming qualityof the projection optical system and coefficients of each term in aZernike polynomial; and deciding an exposure condition whose settingvalues related to the setting information being focused on are optimal,based on the image forming quality calculated for each of the exposureconditions.

When information related to wavefront aberration of the projectionoptical system and the Zernike Sensitivity Chart that denotes a relationbetween image forming quality of the projection optical system andcoefficients of each term in a Zernike polynomial are input into thecomputer that has the program installed, the computer calculates theimage forming quality of the projection optical system under a pluralityof exposure conditions that have different setting values, which arerelated to setting information being focused on among a plurality ofsetting information for the transfer, respectively, in response, anddecides the exposure condition whose setting values related to thesetting information being focused on are optimal, based on the imageforming quality calculated for each of the exposure conditions. Thisallows the computer to execute the process of optimizing the formingstate of the projected image of the pattern on the object smoothly.

According to a fifteenth aspect of the present invention, there isprovided a fourth program of a computer that makes an exposureapparatus, which comprises an adjustment unit that adjusts a formingstate of a projected image of a pattern on an object to transfer thepattern on the object via a projection optical system, execute apredetermined process, the program making the computer execute aprocedure of: deciding an optimal adjustment amount of the adjustmentunit under an exposure condition whose image forming quality of theprojection optical system is optimal, in response to input ofinformation related to wavefront aberration of the projection opticalsystem, a Zernike Sensitivity Chart that denotes a relation between theimage forming quality of the projection optical system and coefficientsof each term in a Zernike polynomial, and a wavefront aberrationvariation table that denotes a relation between adjustment by theadjustment unit and a change in wavefront aberration of the projectionoptical system.

When information related to wavefront aberration of the projectionoptical system, the Zernike Sensitivity Chart that denotes a relationbetween image forming quality of the projection optical system andcoefficients of each term in a Zernike polynomial, and the wavefrontaberration variation table that denotes a relation between adjustment bythe adjustment unit and a change in wavefront aberration of theprojection optical system are input into the computer that has theprogram installed, the computer decides the optimal adjustment amount ofthe adjustment unit under an exposure condition whose image formingquality of the projection optical system is optimal. Accordingly, byadjusting the adjustment unit based on the adjustment amount that hasbeen decided, the computer can execute the process of optimizing theforming state of the projected image of the pattern on the objectsmoothly.

According to a sixteenth aspect of the present invention, there isprovided a fifth program of a computer that makes an exposure apparatus,which transfers a pattern onto an object via a projection opticalsystem, execute a predetermined process, the program making the computerexecute a procedure of: using a Zernike Sensitivity Chart, which isdifferent in at least a part of a plurality of exposure conditions, andalso making at least one Zernike Sensitivity Chart different in at leasta part of the plurality of exposure conditions by interpolationcalculation based on a plurality of other Zernike Sensitivity Charts, oncalculating image forming quality of the projection optical system undera plurality of exposure conditions that have different setting values,which are related to setting information being focused on among aplurality of setting information related to projection conditions of apattern subject to projection by the projection optical system,respectively, in response to input of information related to wavefrontaberration of the projection optical system and a Zernike SensitivityChart that denotes a relation between image forming quality of theprojection optical system and coefficients of each term in a Zernikepolynomial.

When information related to wavefront aberration of the projectionoptical system and the Zernike Sensitivity Chart that denotes a relationbetween image forming quality of the projection optical system andcoefficients of each term in a Zernike polynomial are input into thecomputer that has the program installed, the computer uses the ZernikeSensitivity Chart, which is different in at least a part of a pluralityof exposure conditions, and also makes at least one Zernike SensitivityChart different in at least a part of the plurality of exposureconditions by interpolation calculation based on a plurality of otherZernike Sensitivity Charts, on calculating image forming quality of theprojection optical system under a plurality of exposure conditions thathave different setting values, which are related to setting informationbeing focused on among a plurality of setting information related toprojection conditions of a pattern subject to projection by theprojection optical system, respectively, in response to the input of theabove information. This allows the Zernike Sensitivity Chart under thetarget exposure condition to be obtained even when the ZernikeSensitivity Charts under the plurality of exposure condition are notprepared in advance, by interpolation calculation based on a pluralityof other Zernike Sensitivity Charts. In addition, because the imageforming quality of the projection optical system is calculated undereach of the plurality of exposure condition using the ZernikeSensitivity Charts, the optimal exposure condition can be set, based onthe calculation results.

The first to fifth program of the present invention can be a subject ofmarketing in a recorded state in an information storage medium.Accordingly, from a seventeenth aspect of the present invention, thefirst to fifth program can be an information storage medium that can beread by a computer.

According to an eighteenth aspect of the present invention, there isprovided a making method of a projection optical system that projects apredetermined pattern on an object, the making method comprising: aprocess of assembling the projection optical system by assembling aplurality of optical elements into a barrel in a predeterminedpositional relationship; a process of measuring wavefront aberration ofthe projection optical system after its assembly; a process of adjustingthe projection optical system so as to make the measured wavefrontaberration optimal.

In this case, the making method further comprising: a process ofobtaining information related to a surface shape of each of the opticalelements in prior to the process of assembling, the process ofassembling comprising: obtaining information related to spacing ofoptical surfaces of each of the optical elements being assembled; andthe making method further comprising: a process of correcting a knownoptical basic data, based on the information related to a surface shapeof each of the optical elements and the information related to spacingof optical surfaces of each of the optical elements, and reproducingoptical data during a making process of the projection optical systemthat has been actually assembled, in prior to the process of adjustingthe projection optical system; and a process of correcting an adjustmentbasic database that includes a wavefront aberration variation table,which denotes a relation based on designed values of the projectionoptical system between a unit drive amount of each of the opticalelements in directions of a predetermined degree of freedom and anamount of change in a coefficient of each term in a Zernike polynomialcalculated, based on the optical basic data, and in the process ofadjusting the projection optical system, information on adjustmentamount of each of the optical elements in directions of each degree offreedom is calculated using the database that has been corrected andmeasurement results of the wavefront aberration, and based on results ofthe calculation, at least one of the optical elements is driven in atleast a direction of one degree of freedom.

According to a nineteenth aspect of the present invention, there isprovided a making method of an exposure apparatus that transfers apredetermined pattern on an object via a projection optical system, themaking method comprising: a process of making the projection opticalsystem; a process of assembling the projection optical system that hasbeen made into an exposure apparatus main body; a process of measuringwavefront aberration of the projection optical system in a state wherethe projection optical system has been assembled into the exposureapparatus main body; and a process of calculating information onadjustment amount of each of optical elements in directions of eachdegree of freedom using a database that includes a wavefront aberrationvariation table, which denotes a relation based on designed values ofthe projection optical system between a unit drive amount of each of theoptical elements in directions of a predetermined degree of freedom andan amount of change in a coefficient of each term in a Zernikepolynomial calculated, and the wavefront aberration that has beenmeasured, and based on results of the calculation, at least one of theoptical elements is driven in at least a direction of one degree offreedom.

According to a twentieth aspect of the present invention, there isprovided an image forming quality measuring method of a projectionoptical system that projects a pattern on an object wherein a ZernikeSensitivity Chart, which is different in at least a part of a pluralityof conditions, is used, and also at least one of the Zernike SensitivityChart which is different is made by interpolation calculation based on aplurality of other Zernike Sensitivity Charts, on calculating imageforming quality of the projection optical system under a plurality ofconditions that have different setting values, which are related tosetting information being focused on among a plurality of settinginformation related to the projection, respectively, based oninformation related to wavefront aberration of the projection opticalsystem and a Zernike Sensitivity Chart that denotes a relation betweenimage forming quality of the projection optical system and coefficientsof each term in a Zernike polynomial.

In this case, the plurality of setting information can includeinformation related to projection conditions of a pattern subject toprojection by the projection optical system.

In this case, the information related to the projection conditionsincludes optical information of the projection optical system and thatof an illumination optical system illuminating the pattern.

In the image forming quality measuring method in the present invention,the plurality of setting information can include information related toa pattern subject to projection by the projection optical system.

In addition, in a lithographic process, by performing exposure using anyone of the first to fourth exposure methods, the pattern can be formedwith good accuracy on the object, which in turn allows highly integratedmicrodevices to be produced with good yield. Accordingly, further fromanother aspect, the present invention can also be referred to as adevice manufacturing method that uses any one of the first to fourthmethods in the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings;

FIG. 1 is a view showing a configuration of a computer system related toan embodiment of the present invention;

FIG. 2 is a view showing the entire configuration of a first exposureapparatus 922 ₁ in FIG. 1;

FIG. 3 is a sectional view of an example of a wavefront aberrationmeasuring instrument;

FIG. 4A is a view showing beams emitted from a microlens array whenthere is no aberration in an optical system, and FIG. 4B is a viewshowing beams emitted from a microlens array when there is aberration inan optical system;

FIG. 5 is a flowchart showing a processing algorithm executed by a CPUin a second communications server;

FIG. 6 is a flow chart (No. 1) showing a processing in step 118 in FIG.5;

FIG. 7 is a flow chart (No. 2) showing a processing in step 118 in FIG.5;

FIG. 8 is a flow chart (No. 3) showing a processing in step 118 in FIG.5;

FIG. 9 is a flow chart (No. 4) showing a processing in step 118 in FIG.5;

FIG. 10 is a flow chart (No. 5) showing a processing in step 118 in FIG.5;

FIG. 11 is a schematic diagram for showing an interpolation method tomake a ZS file;

FIG. 12 is a view modeling a processing when a restraint condition isviolated;

FIG. 13 is a view showing the arrangement of a drive axis of a movablelens 13 _(i);

FIG. 14 is a flow chart (No. 1) showing a processing in step 116 in FIG.5;

FIG. 15 is a flow chart (No. 2) showing a processing in step 116 in FIG.5;

FIG. 16 is a flow chart (No. 3) showing a processing in step 116 in FIG.5;

FIG. 17 is a flow chart (No. 4) showing a processing in step 116 in FIG.5;

FIG. 18 is a flow chart (No. 5) showing a processing in step 116 in FIG.5;

FIG. 19 is a flow chart (No. 1) showing a processing in step 120 in FIG.5;

FIG. 20 is a flow chart (No. 2) showing a processing in step 120 in FIG.5;

FIG. 21 is a flow chart showing the entire making process of aprojection optical system; and

FIG. 22 is a view showing a configuration of a computer system relatedto a modified example.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, an embodiment of the present invention is described,referring to FIGS. 1 to 21.

FIG. 1 shows an entire configuration of a computer system serving as animage forming state adjusting system related to an embodiment of thepresent invention.

A computer system 10 shown in FIG. 1 is an intranet system built in asemiconductor factory of a device manufacturer (hereinafter referred toas ‘manufacturer A’ as appropriate) that uses equipment such as exposureapparatus for manufacturing devices. This computer system 10 comprises alithographic system 912 arranged within a clean room that includes afirst communications server 920, and a second communications server 930connecting to the first communications server 920 structuringlithographic system 912 via a local area network (LAN) 926 serving as acommunications channel.

Lithographic system 912 is made up including the first communicationsserver 920, a first exposure apparatus 922 ₁, a second exposureapparatus 922 ₂, and a third exposure apparatus 922 ₃ (hereinafterreferred to as ‘exposure apparatus 922’ as appropriate) connectingreciprocally via a LAN 918.

FIG. 2 shows an entire structure of the first exposure apparatus 922 ₁.Exposure apparatus 922 ₁ is a reduction projection exposure apparatusbased on a step-and-repeat method, using a pulsed laser light source asan exposure light source (hereinafter referred to as ‘light source’).

Exposure apparatus 922 ₁ comprises the following parts: an illuminationsystem composed of a light source 16 and an illumination optical system12; a reticle stage RST serving as a mask stage that holds a reticle Ras a mask illuminated by an exposure illumination light EL serving as anenergy beam from the illumination system; a projection optical system PLthat projects illumination light EL outgoing from reticle R on a wafer W(on an image plane) serving as an object; a wafer stage WST on which a Ztilt stage 58 serving as an object stage that holds wafer W is mounted;a control system for these parts, and the like.

As light source 16, in this case, a pulsed ultraviolet light source thatemits a pulsed light in the vacuum ultraviolet region such as an F₂laser (output wavelength 157 nm) or an ArF excimer laser (outputwavelength 193 nm) is used. Incidentally, as light source 16, a lightsource that emits a pulsed light in the far ultraviolet region such as aKrF excimer laser (output wavelength 248 nm) or in the ultravioletregion may also be used.

In actual, light source 16 is arranged in a separate room, which is aservice room having a lower degree of cleanliness than that of a cleanroom where a chamber 11 that houses the exposure apparatus main bodycomposed of components of illumination optical system 12, reticle stageRST, projection optical system PL, wafer stage WST, and the like isarranged. Light source 16 connects to chamber 11 via a lighttransmitting optical system (not shown), which includes at least anoptical system for optical axis adjustment called a beam matching unitin a part of its system. Light source 16 controls the on/off of theoutput of laser beam LB, the energy of laser beam LB per pulse, theoscillation frequency (the repetition frequency), the center wavelengthand the spectral line half width (wavelength width), and the like by aninternal controller, based on control information TS from a maincontroller 50.

Illumination optical system 12 comprises the following parts: a beamshaping illuminance unifying optical system 20, which includes acylinder lens, a beam expander (none of which are shown), and an opticalintegrator (homogenizer) 22; an illumination system aperture stop plate24; a first relay lens 28A; a second relay lens 28B; a reticle blind 30;an optical path bending mirror M; a condenser lens 32, and the like. Asthe optical integrator, a fly-eye lens, a rod integrator (an internalreflection type integrator), or a diffractive optical element can beused. In the embodiment, a fly-eye lens is used as optical integrator22; therefore, hereinafter it will also be referred to as fly-eye lens22.

Beam shaping illuminance unifying optical system 20 connects to a lighttransmitting optical system (not shown) via a light transmitting window17 provided in chamber 11. Beam shaping illuminance unifying opticalsystem 20 shapes the sectional shape of laser beam LB, which is thepulsed light emitted from light source 16 that enters beam shapingilluminance unifying optical system 20 via light transmitting window 17,using parts such as a cylinder lens or a beam expander. Then, when thelaser beam enters beam shaping illuminance unifying optical system 20,fly-eye lens 22, which is located inside beam shaping illuminanceunifying optical system 20 on the outgoing side, forms an area lightsource (a secondary light source), which is composed of multiple pointsources on the focusing plane on the outgoing side of the laser beamarranged so that it substantially coincides with the pupil plane ofillumination optical system 12, so as to illuminate reticle R withuniform distribution. Hereinafter, the laser beam outgoing from thesecondary light source will be referred to as ‘illumination light EL’.

In the vicinity of the focusing plane on the outgoing side of fly-eyelens 22 illumination system aperture stop plate 24 is disposed, made ofa circular plate shaped member. In illumination system aperture stopplate 24, for example, the following aperture stops are formed spacedsubstantially apart at an equal angle: a conventional aperture stop madeup of a circular aperture (conventional aperture); an aperture stop madeup of small circular apertures to reduce a σ value, which is a coherencefactor (small σ aperture); a ring shaped aperture stop for annularillumination (ring-shaped aperture); and a modified aperture stop madeup of a plurality of apertures arranged eccentrically to a modifiedlight source method (FIG. 1 shows only two types of apertures).Illumination system aperture stop plate 24 rotates by a drive unit 40such as a motor or the like that operates under the control of maincontroller 50, so that an aperture stop is selectively set on theoptical path of illumination light EL, and the shape of the light sourceplane in Koehler illumination is limited to shapes such as annular,small circles, large circle, or quadrupole.

Instead of, or combined with aperture stop plate 24, for example, anoptical unit that includes at least one of a plurality of diffractiveoptical elements arranged switchable in the illumination optical systemthat disperse the illumination light in different areas on the pupilplane of the illumination optical system, a plurality of prisms (such asa cone prism or a polyhedral prism) that has at least one prism movablealong an optical axis IX of the illumination optical system, that is,the spacing in the optical axis direction of the illumination opticalsystem is variable, and a zoom optical system may be arranged in betweenlight source 16 and optical integrator 22. And, by making the intensitydistribution of the illumination light on the entering surface variablewhen optical integrator 22 is a fly-eye lens, or by making the angle ofincidence of the illumination light to the entering surface variablewhen optical integrator 22 is an internal reflection type integrator,the light quantity distribution of the illumination light on the pupilplane of the illumination optical system (the size and shape of thesecondary light source), that is, the light quantity loss due to changein illumination conditions of reticle R, is preferably suppressed. Inthe embodiment, a plurality of light source images (virtual images)formed by the internal reflection type integrator will also be referredto as the secondary light source.

On the optical path of illumination light EL outgoing from illuminationsystem aperture stop plate 24, a relay optical system is arranged,composed of a first relay lens 28A and a second relay lens 28B withreticle blind 30 disposed in between. Reticle blind 30 is arranged on asurface conjugate to the pattern surface of reticle R, and a rectangularaperture is formed thereon that sets a rectangular shaped illuminationarea IAR on reticle R. As reticle blind 30, a movable blind whoseaperture shape is variable is used, and its aperture is set by maincontroller 50, based on a blind setting information that is also calledmasking information.

On the optical path of illumination light EL in the rear of the secondrelay lens 28B, bending mirror M is disposed that reflects illuminationlight EL that has passed through the second relay lens 28B towardsreticle R, and in the rear of mirror M on the optical path ofillumination light EL, condenser lens 32 is disposed.

In the arrangement described so far, the entering surface of fly-eyelens 22, the disposal surface of reticle blind 30, and the patternsurface of reticle R are set optically conjugate with one another, whilethe light source plane formed on the focusing plane (the pupil plane ofthe illumination optical system) on the outgoing side of fly-eye lens 22and the Fourier transform plane (outgoing pupil plane) of projectionoptical system PL are set optically conjugate, making up a Koehlerillumination system.

The operation of the illumination system having such an arrangement willnow be briefly described. With the system, laser beam LB, which is thepulsed light emitted from light source 16, enters fly-eye lens 22 afterentering beam shaping illuminance unifying optical system 20 where its'sectional shape is shaped. With this operation, the secondary lightsource previously described is formed on the focusing plane on theoutgoing side of the fly-eye lens 22.

After illumination light EL emitted from the above secondary lightsource passes through one of the apertures formed in illumination systemaperture stop plate 24, it passes through the rectangular aperture ofreticle blind 30 via the first relay lens 28A, and then passes throughthe second relay lens 28B. Then the optical path of illumination lightEL is bent perpendicularly downward by mirror M, and illumination lightEL then proceeds through condenser lens 32 and illuminates therectangular illumination area IAR of reticle R held on reticle stage RSTwith uniform illuminance distribution.

On reticle stage RST, reticle R is mounted and held by suction viaelectrostatic chucking (or vacuum chucking) or the like (not shown).Reticle stage RST has a structure so that it can be finely driven(including rotation) within a horizontal plane (an XY plane) by a drivesystem (not shown). Incidentally, the position of reticle stage RST ismeasured at a predetermined resolution (for example, a resolution ofapproximately 0.5 to 1 nm) with a position detector such as a reticlelaser interferometer (not shown), and the measurement results aresupplied to main controller 50.

The material used for reticle R needs to be different depending on thelight source that is used. That is, when an ArF excimer laser or a KrFexcimer laser is used as the light source, materials such as syntheticquartz, fluoride crystal as in fluorite, or fluorine-doped quartz can beused, however, when an F₂ laser is used, the reticle has to be made offluoride crystal such as fluorite, or fluorine-doped quartz.

Projection optical system PL is, for example, a double telecentricreduction system. The projection magnification of projection opticalsystem PL is for example, ¼, ⅕, or ⅙. Therefore, when illumination areaIAR on reticle R is illuminated with illumination light EL as ispreviously described, the pattern formed on reticle R is projected andtransferred on a rectangular exposure area IA (normally coincides withthe shot area) on wafer W whose surface is coated with a resist(photosensitive agent), as an image reduced by the projectionmagnification by projection optical system PL.

As is shown in FIG. 2, as projection optical system PL, a refractionsystem consisting only of a plurality of refraction optical elements(lens elements) 13, such as from 10 to 20 pieces, is used. Of theplurality of lens elements 13 that make up projection optical system PL(in this case, 5 lenses in order to simplify the description), lenselements 13 ₁, 13 ₂, 13 ₃, 13 ₄, and 13 ₅ disposed on the object surfaceside (reticle R side) are movable lenses that can be moved from theoutside by an image forming quality correction controller 48. Lenselements 13 ₁ to 13 ₅ are each held by the barrel via lens holders thathave a double structure (not shown). These lens elements 13 ₁ to 13 ₅are each held by inner lens holders, and these inner lens holders aresupported by drive elements (not shown) such as piezo elements at threepoints in the gravitational direction with respect to outer lensholders. And, by independently adjusting the applied voltage to thedrive elements, each of the lens elements 13 ₁ to 13 ₅ can be shiftedalong a Z-axis direction which is the optical axis direction ofprojection optical system PL, and the lens elements can be driven in adirection of inclination (that is, a rotational direction around theX-axis (θx) and a rotational direction around the Y-axis (θy)) withrespect to an XY plane.

The barrel normally holds lens elements 13 besides those referred toabove via lens holders. Optical elements other than lens elements 13 ₁to 13 ₅ may be made drivable, such as the lenses disposed in thevicinity of the pupil plane of projection optical system PL, the lensesdisposed on the image plane side, or an aberration correction plane(optical plate) that corrects the aberration of projection opticalsystem PL, especially the non-rotational symmetric component.Furthermore, the degree of freedom (the movable direction) of suchdrivable optical elements is not limited to three, and may be one, two,or four and over.

In addition, a pupil aperture stop 15 that can continuously change thenumerical aperture (N.A.) within a predetermined range is provided inthe vicinity of the pupil plane of projection optical system PL. Aspupil aperture stop 15, for example, the so-called iris diaphragm isused, which operates under the control of main controller 50.

When the ArF excimer laser beam or the KrF excimer laser beam is used asillumination light EL, synthetic quartz can also be used besidesmaterials such as fluoride crystal as in fluorite, or fluorine-dopedquartz can be used for each lens elements structuring projection opticalsystem PL, however, when the F₂ laser is used, the reticle has to bemade of fluoride crystal such as fluorite, or fluorine-doped quartz.

Wafer stage WST is driven freely within the XY two-dimensional plane bya wafer stage drive section 56 including a linear motor or the like. OnZ tilt stage 58 mounted on wafer stage WST, wafer W is held byelectrostatic suction (or vacuum chucking) or the like via a waferholder (not shown).

In addition, Z tilt stage 58 is made so that the position in the XYdirection on wafer stage WST is set and can also be moved along theZ-axis direction by a drive system (not shown) as well as being drivable(tiltable) in a direction of inclination (that is, the rotationaldirection around the X-axis (θx) and a rotational direction around theY-axis (θy)) with respect to the XY plane. Such an arrangement sets thesurface position of wafer W (the Z-axis position and the inclinationwith respect to the XY plane) held on Z tilt stage 58 at a desiredstate.

Furthermore, a movable mirror 52W is fixed on Z tilt stage 58, and theposition of Z tilt stage 58 in the X-axis direction, the Y-axisdirection, and the θz direction (the rotational direction around theZ-axis) is measured with a wafer laser interferometer 54W externallyarranged. The positional information measured by interferometer 54W issent to main controller 50, which controls wafer stage WST (and Z tiltstage 58) based on the measurement results via wafer stage drive section56 (which includes both the drive system of wafer stage WST and thedrive system of Z tilt stage 58). Incidentally, instead of providingmovable mirror 52W, for example, the end surface (side surface) of Ztilt stage 58 polished into a reflection surface may be used.

In addition, on Z tilt stage 58, a fiducial mark plate FM is fixed onwhich reference marks such as reference marks for the so-called baselinemeasurement by the alignment system ALG (to be described later) areformed, so that its surface is substantially at the same height as thesurface of wafer W.

In addition, on the side surface of Z tilt stage 58 on the +X side (onthe right side within the page surface of FIG. 2), a wavefrontaberration measuring instrument 80 is attached, serving as a detachableportable wavefront measuring unit.

As is shown in FIG. 3, wavefront aberration measuring instrument 80comprises a hollow casing 82, a photodetection optical system 84 made upof a plurality of optical elements arranged at a predeterminedpositional relationship within casing 82, and a photodetection portion86 disposed on the +Y end inside casing 82.

Casing 82 is made from a member that has an L-shaped section in the YZplane and a space formed inside. The uppermost portion (the end portionin the +Z direction) has an opening 82 a of a circular shape in a planarview (when viewed from above) so that the light from above casing 82proceeds into the space inside. In addition, a cover glass 88 isprovided to cover opening 82 a from the inside of casing 82. On theupper surface of cover glass 88, a light shielding membrane that has acircular opening in the center is formed by vapor deposition of metalsuch as chrome, which shields unnecessary light from enteringphotodetection optical system 84 when the wavefront aberration ofprojection optical system PL is measured.

Photodetection optical system 84 is made up of an objective lens 84 a, arelay lens 84 b, and a deflecting mirror 84 c, which are sequentiallyarranged from under cover glass 88 inside casing 82 in a downwarddirection, and a collimator lens 84 d and a microlens array 84 e, whichare sequentially arranged on the +Y side of deflecting mirror 84 c.Deflecting mirror 84 c is provided having an inclination of 45°, and bydeflecting mirror 84 c, the optical path of the light entering theobjective lens 84 a from above in a downward vertical direction isdeflected toward the collimator lens 84 d. Each of the optical membersthat make up photodetection optical system 84 is fixed to the wall ofcasing 82 on the inner side, via holding members (not shown),respectively. Microlens array 84 e has a plurality of small convexlenses (lens elements) that are arranged in an array shape on a planeperpendicular to the optical path.

Photodetection portion 86 is made up of parts like a photodetectionelement such as a two-dimensional CCD, and an electric circuit such as acharge transport controlling circuit. The photodetection element has anarea large enough to receive all the beams that have entered objectivelens 84 a and are outgoing microlens array 84 e. The measurement data ofphotodetection portion 86 is output to main controller 50 via a signalline (not shown) or by radio transmission.

Using the above wavefront aberration measuring instrument 80 allows thewavefront aberration of projection optical system PL to be measured onbody. The measuring method of the wavefront aberration using wavefrontaberration measuring instrument 80 will be described later in thedescription.

Referring back to FIG. 2, in exposure apparatus 922 ₁ in the embodiment,a multiple point focus position detection system based on an obliqueincident method (hereinafter simply referred to as a ‘focus detectionsystem’) is provided. The system is made up of an irradiation system 60a, which has a light source whose on/off operation is controlled by maincontroller 50 and irradiates an imaging beam toward the image formingplane of projection optical system PL from an oblique direction againstthe optical axis AX for forming multiple pinholes or slit images, and aphotodetection optical system 60 b that receives the reflection beams ofthe imaging beam reflected off the surface of wafer W. As the focusdetection system (60 a and 60 b), a unit having the same structure asthe one disclosed in, for example, Japanese Patent Application No.H05-275313 and its corresponding U.S. Pat. No. 5,502,311, is used. Aslong as the national laws in designated states or elected states, towhich this international application is applied, permit, the disclosuresof the above publication and the above U.S. patent are incorporatedherein by reference.

On exposure or the like, main controller 50 performs auto-focusing(automatic focusing) and auto-leveling based on defocus signals such asS-curve signals from photodetection optical system 60 b so that thedefocus becomes zero by controlling the Z position and the inclinationwith respect to the XY plane of wafer W via wafer stage drive section56. In addition, when wavefront aberration is measured in the mannerthat will be described later in the description, main controller 50measures and aligns the Z position of wavefront aberration measuringinstrument 80 using the focus detection system (60 a and 60 b). Uponthis operation, the inclination of wavefront aberration measuringinstrument 80 may also be measured if necessary.

Furthermore, exposure apparatus 922 ₁ comprises alignment system ALGbased on an off-axis method, which is used for measuring the alignmentmarks on wafer W held on wafer stage WST and the position of thereference marks formed on fiducial mark plate FM. As alignment systemALG, a sensor of an FIA (Field Image Alignment) system based on an imageprocessing method is used that uses an image pickup device (such as aCCD) to pick up images of a subject mark on a photodetection surfaceformed by irradiating a broadband detection beam on the subject mark sothat the mark will not be exposed and outputs the pick-up signals.Besides the sensor of the FIA system, a sensor that detects scatteredlight or diffracted light generated from a subject mark when the subjectmark is irradiated with a coherent detection beam, or a sensor that alight of two diffracted lights (such as in the same order) generatedfrom the subject mark and made to interfere with each other can be usedindependently, or in a combined arrangement.

Furthermore, although it is omitted in the drawings, in exposureapparatus 922 ₁ in the embodiment, above reticle R, a pair of reticlealignment systems is provided, which is made up of a TTR (Through TheReticle) alignment optical system that uses light of the exposurewavelength in order to observe reticle marks formed on reticle R and thecorresponding reference marks on the fiducial mark plate at the sametime via projection optical system PL. In the embodiment, as waferalignment system ALG and the reticle alignment system, units having thesame structure as the ones disclosed in, for example, Japanese PatentApplication Laid-open No. H06-97031 and its corresponding U.S. Pat. No.6,198,527 are used. As long as the national laws in designated states orelected states, to which this international application is applied,permit, the disclosures of the above publication and the above U.S.patent are incorporated herein by reference.

In FIG. 2, the control system is mainly composed of main controller 50.Main controller 50 is made up of a so-called workstation (ormicrocomputer) comprising a CPU (Central Processing Unit), ROM (ReadOnly Memory), RAM (Random Access Memory), or the like, and controls theoverall operation such as the stepping of wafer stage WST in betweenshots and the exposure timing so that exposure operations areappropriately performed.

In addition, for example, a storage unit 42 made up of a hard disk, aninput unit 45 comprising a key board and a pointing-device such as amouse, a display unit 44 such as a CRT display (or liquid-crystaldisplay), and a drive unit 46 which is an information recording mediumsuch as a CD (compact disc), a DVD (digital versatile disc), an MO(magneto-optical disc), or an FD (floppy disc) externally connects tomain controller 50. Furthermore, LAN 918 referred to earlier alsoconnects to main controller 50.

In storage unit 42, wavefront aberration measurement data of thestand-alone projection optical system PL (hereinafter referred to as a‘stand-alone wavefront aberration’) is stored, which is measured at themaking stage of the exposure apparatus before projection optical systemPL is incorporated into the exposure apparatus main body, by forexample, a wavefront aberration measuring unit called a PMI (PhaseMeasurement Interferometer).

In addition, in storage unit 42, data on wavefront aberration measuredby wavefront aberration measuring instrument 80 or a wavefrontaberration correction amount data (difference between the wavefrontaberration and the stand-alone wavefront aberration), and information onthe adjustment amount, that is, the positional information of each ofmovable lenses 13 ₁ to 13 ₅ in directions of three degrees of freedom,the positional information of wafer W in directions of three degrees offreedom, and the information on the wavelength of the illumination lightis stored. The above data of wavefront aberration is measured in a statewhere the position of each of movable lenses 13 ₁ to 13 ₅ in directionsof three degrees of freedom, the Z position and inclination of wafer W(Z tilt stage 58), and a wavelength λ of the illumination light areadjusted so that, for example, the forming state of an image on wafer Wprojected by projection optical system PL becomes optimal (such as, whenthe aberration is zero or under a permissible value) under a pluralityof reference exposure conditions that will be described later. Thereference exposure conditions, in this case, are ID controlled, eachexposure condition serving as identifying information. Therefore,hereinafter, each of the reference exposure conditions will be referredto as reference ID. That is, in the storage unit, the information onadjustment amount of a plurality of reference IDs and the data onwavefront aberration or wavefront aberration correction amount isstored.

In the information storage medium (a CD-ROM in the following descriptionfor the sake of convenience) set in drive unit 46, a conversion programis stored for converting the positional deviation measured usingwavefront aberration measuring instrument 80 into coefficients of theterms in the Zernike polynomial.

The second exposure apparatus 922 ₂ and the third exposure apparatus 922₃ have a structure similar to that of the above first exposure apparatus922 ₁.

Next, the measuring method of the wavefront aberration of the first tothird exposure apparatus 922 ₁ to 922 ₃ performed during maintenance orthe like will be described. In the following description, for the sakeof simplicity, the aberration of photodetection optical system 84 inwavefront aberration measuring instrument 80 is to be small enough to beignored.

As a premise, the conversion program stored in the CD-ROM set in driveunit 46 is to be installed into storage unit 42.

During normal exposure, because wavefront aberration measuringinstrument 80 is detached from Z tilt stage 58, when the wavefrontaberration measurement is performed the operator or the servicetechnician or the like (hereinafter referred to as ‘operator or thelike’ as appropriate) attaches wavefront aberration measuring instrument80 onto the side surface of Z tilt stage 58. In this operation,wavefront aberration measuring instrument 80 is fixed onto apredetermined reference surface (in this case, the surface on the +Xside) via a bolt or a magnet or the like, so that when the wavefront ismeasured, wavefront aberration measuring instrument 80 is within themovement strokes of wafer stage WST (Z tilt stage 58).

When the above attachment is completed, main controller 50 moves waferstage WST via wafer stage drive section 56 so that wavefront aberrationmeasuring instrument 80 is positioned under alignment system ALG, inresponse to a command to start measurement input by the operator or thelike. Then, main controller 50 makes alignment system ALG detect thealignment marks provided in wavefront aberration measuring instrument 80(not shown), and based on the detection results and the measurementvalues of laser interferometer 54W at that point, main controller 50calculates the position coordinates of the alignment marks and obtainsthe accurate position of wavefront aberration measuring instrument 80.When the position of wavefront aberration measuring instrument 80 hasbeen measured, then main controller 50 measures the wavefront aberrationin the manner described below.

First of all, main controller 50 loads a measurement reticle (notshown)(hereinafter referred to as a ‘pinhole reticle’) on which pinholepatterns are formed onto reticle stage RST using a reticle loader (notshown). The pinhole reticle is a reticle on which pinholes (pinholesthat become substantially ideal point light sources and generatespherical waves) are formed on its surface at a plurality of points inthe same area as illumination area IAR.

In the pinhole reticle used in this case, by making the distribution oflight from the pinhole patterns cover substantially the whole pupilplane, for example, by providing a diffusing surface on its uppersurface, the wavefront aberration can be measured on the entire pupilplane of projection optical system PL. In the embodiment, since pupilaperture stop 15 is provided in the vicinity of the pupil plane ofprojection optical system PL, the wavefront aberration will actually bemeasured on the pupil plane set by pupil aperture stop 15.

After the pinhole reticle has been loaded, main controller 50 detectsthe reticle alignment marks formed on the pinhole reticle using thereticle alignment system, and based on the detection results, aligns thepinhole reticle at a predetermined position. With this operation, thecenter of the pinhole reticle substantially coincides with the opticalaxis of projection optical system PL.

Then, main controller 50 sends control information TS to light source 16to start emission of laser beam LB. With this operation, illuminationlight EL from illumination optical system 12 irradiates the pinholereticle. The lights outgoing from the plurality of pinholes of thepinhole reticle then condense on the image plane via projection opticalsystem PL and form images of the pinholes on the image plane.

Next, main controller 50 moves wafer stage WST via wafer stage drivesection 56 while monitoring the measurement values of wafer laserinterferometer 54W, so that an image forming point where an image of apinhole of the pinhole reticle (hereinafter referred to as the ‘focusedpinhole’) is formed substantially coincides with the center of opening82 a in wavefront aberration measuring instrument 80. When performingsuch an operation, main controller 50 finely moves Z tilt stage 58 inthe Z-axis direction via wafer stage drive section 56 based on thedetection results of focus detection system (60 a and 60 b), so as tomake the upper surface of cover glass 88 in wavefront aberrationmeasuring instrument 80 coincide with the image plane where the pinholeimage is formed. In this case, the angle of inclination of wafer stageWST is also adjusted if necessary. With the above operations, theimaging beams of the focused pinhole enters photodetection opticalsystem 84 via the opening in the center of cover glass 88, and isreceived by the photodetection elements that make up photodetectionportion 86.

More particularly, the focused pinhole on the pinhole reticle generatesspherical waves, which become parallel beams that irradiate microlensarray 84 e, via projection optical system PL and objective lens 84 a,relay lens 84 b, mirror 84 c, and collimator lens 84 d that make upphotodetection optical system 84 of wavefront aberration measuringinstrument 80. When the parallel beams irradiate microlens array 84 e,the pupil plane of projection optical system PL is relayed and dividedby microlens array 84 e. Each lens element of microlens array 84 econdenses the lights (divided light) on the photodetection surface ofthe photodetection element, and the images of the pinhole are eachformed on the photodetection surface.

In this case, when projection optical system PL is an ideal opticalsystem that does not have any wavefront aberration, the wavefront in thepupil plane of projection optical system PL becomes an ideal shape (inthis case, a planar surface), and as a consequence, the parallel beamsentering microlens array 84 e is supposed to be a plane wave that has anideal wavefront. In this case, as is shown in FIG. 4A, a spot image(hereinafter also referred to as a ‘spot’) is formed at a position onthe optical axis of each lens element that make up microlens array 84 e.

However, because projection optical system PL normally has wavefrontaberration, the wavefront of the parallel beams incident on microlensarray 84 e deviates from the ideal wavefront, and corresponding to thedeviation, that is, the inclination of the wavefront with respect to theideal wavefront, the image forming position of each spot deviates fromthe position on the optical axis of each lens element of microlens array84 e, as is shown in FIG. 4B. In this case, the positional deviation ofeach spot from its reference point (the position on the optical axis ofeach lens element) corresponds to the inclination of the wavefront.

Then, the lights incident on each of the condensing points on thephotodetection element making up photodetection portion 86 (beams of thespot images) are photoelectrically converted at the photodetectionelement, and the photoelectric conversion signals are sent to maincontroller 50 via the electric circuit. Based on the photodetectionconversion signals, main controller 50 calculates the image formingposition of each spot, and furthermore, calculates the positionaldeviation (Δξ, Δη) using the calculation results and the positional dataof the known reference points, and stores it in the RAM. During suchoperation, the measurement values of laser interferometer 54W at theabove point (Xi, Yi) are sent to main controller 50.

When measurement of positional deviation of the spot images by wavefrontaberration measuring instrument 80 at the image forming point of thefocused pinhole image is completed in the manner described above, maincontroller 50 moves wafer stage WST so that the substantial center ofopening 82 a of wavefront aberration measuring instrument 80 coincideswith the image forming point of the next pinhole image. When thismovement is completed, main controller 50 makes light source 16 generatelaser beam LB as is previously described, and similarly calculates theimage forming position of each spot. Hereinafter, a similar measurementis sequentially performed at the image forming point of other pinholeimages.

When all the necessary measurements have been completed in the mannerdescribed above, the data on positional deviation (Δξ, Δη) of eachpinhole image at the image forming point previously described and thecoordinate data of each image forming point (the measurement values oflaser interferometer 54W (Xi, Yi) when performing measurement the imageforming point of each pinhole image) is stored in the RAM of maincontroller 50. During the above measurement, for example, the positionand size of the illumination area on the reticle per pinhole can bechanged using reticle blind 30, so that only the focused pinhole on thereticle, or only the area including the focused pinhole is illuminatedby illumination light EL.

Next, main controller 50 loads the conversion program into the mainmemory. Then, according to the conversion program, main controller 50calculates the wavefront (wavefront aberration) corresponding to theimage forming point of the pinhole images, that is, the wavefrontcorresponding to each of the measurement points from the 1^(st)measurement point to the n^(th) measurement point within the field ofprojection optical system PL, in this case, the coefficients of theterms in the Zernike polynomial in equation (3) that will be describedlater in the description, such as from coefficient Z₁ of the 1^(st) termto coefficient Z₃₇ of the 37^(th) term, based on the positionaldeviation data (Δξ, Δη) for the image forming point of each pinholeimages stored in the RAM and the coordinate data for each image formingpoint, according to the following principle.

In the embodiment, the wavefront of projection optical system PL isobtained by calculation according to the conversion program, based onthe above positional deviations (Δξ, Δη). That is, positional deviations(Δξ, Δη) are values that reflect the gradient of the wavefront withrespect to an ideal wavefront, which on the contrary means that thewavefront can be reproduced based on the positional deviation (Δξ, Δη).As is obvious from the above physical relation between the positionaldeviations (Δξ, Δη) and the wavefront, the principle of this embodimentfor calculating the wavefront is the known Shack-Hartmann wavefrontcalculation principle.

Next, the method of calculating the wavefront based on the abovepositional deviations will be briefly described.

As is described above, the positional deviations (Δξ, Δη) correspond tothe gradient of the wavefront, and by integrating them the shape of thewavefront (or to be more precise, deviations from the reference plane(the ideal wavefront)) is obtained. When the wavefront (deviations fromthe reference plane) is expressed as W(x,y) and the proportionalcoefficient is expressed as k, then the relation in the followingequations (1) and (2) exist.

$\begin{matrix}{{\Delta\;\xi} = {k\frac{\partial W}{\partial x}}} & (1) \\{{\Delta\;\eta} = {k\frac{\partial W}{\partial y}}} & (2)\end{matrix}$

Because it is not easy to integrate the gradient of the wavefront givenonly at spot positions, the surface shape is expanded in series so thatit fits the wavefront. In this case, an orthogonal system is to bechosen for the series. The Zernike polynomial is a series suitable forexpanding an axially opposite surface, expanding in a trigonometricseries in the circumferential direction. That is, when wavefront W isexpressed using a polar coordinate system (ρ, θ), the Zernike polynomialis expanded as is shown in equation (3).

$\begin{matrix}{{W\left( {\rho,\theta} \right)} = {\sum\limits_{i}{Z_{i} \cdot {f_{i}({\rho\theta})}}}} & (3)\end{matrix}$

Because the system is an orthogonal system, coefficient Z_(i) of theterms can be decided independently. Cutting off _(i) at a suitable valuecorresponds to performing a kind of filtering. Table 1 is an exampleshowing the values of f_(i) from the 1^(st) term to the 37^(th) term,along with Zi. In the actual Zernike polynomial, the 37^(th) term inTable 1 corresponds to the 49^(th) term, however, in this description,it will be handled as i=37 (the 37^(th) term). That is, in theinvention, the number of terms in the Zernike polynomial is not limitedin particular.

TABLE 1 Z_(i) f_(i) Z₁ 1 Z₂ ρ cos θ Z₃ ρ sin θ Z₄ 2ρ² − 1 Z₅ ρ² cos 2θZ₆ ρ² sin 2θ Z₇ (3ρ³ − 2ρ) cos θ Z₈ (3ρ³ − 2ρ) sin θ Z₉ 6ρ⁴ − 6ρ² + 1Z₁₀ ρ³ cos 3θ Z₁₁ ρ³ sin 3θ Z₁₂ (4ρ⁴ − 3ρ²) cos 2θ Z₁₃ (4ρ⁴ − 3ρ²) sin2θ Z₁₄ (10ρ⁵ − 12ρ³ + 3ρ) cos θ Z₁₅ (10ρ⁵ − 12ρ³ + 3ρ) sin θ Z₁₆ 20ρ⁶ −30ρ⁴ + 12ρ² − 1 Z₁₇ ρ⁴ cos 4θ Z₁₈ ρ⁴ sin 4θ Z₁₉ (5ρ⁵ − 4ρ³) cos 3θ Z₂₀(5ρ⁵ − 4ρ³) sin 3θ Z₂₁ (15ρ⁶ − 20ρ⁴ + 6ρ²) cos 2θ Z₂₂ (15ρ⁶ − 20ρ⁴ +6ρ²) sin 2θ Z₂₃ (35ρ⁷ − 60ρ⁵ + 30ρ³ − 4ρ) cos θ Z₂₄ (35ρ⁷ − 60ρ⁵ + 30ρ³− 4ρ) sin θ Z₂₅ 70ρ⁸ − 140ρ⁶ + 90ρ⁴ − 20ρ² + 1 Z₂₆ ρ⁵ cos 5θ Z₂₇ ρ⁵ sin5θ Z₂₈ (6ρ⁶ − 5ρ⁴) cos 4θ Z₂₉ (6ρ⁶ − 5ρ⁴) sin 4θ Z₃₀ (21ρ⁷ − 30ρ⁵ +10ρ³) cos 3θ Z₃₁ (21ρ⁷ − 30ρ⁵ + 10ρ³) sin 3θ Z₃₂ (56ρ⁸ − 105ρ⁶ + 60ρ⁴ −10ρ²) cos 2θ Z₃₃ (56ρ⁸ − 105ρ⁶ + 60ρ⁴ − 10ρ²) sin 2θ Z₃₄ (126ρ⁹ −280ρ⁷ + 210ρ⁵ − 60ρ³ + 5ρ) cos θ Z₃₅ (126ρ⁹ − 280ρ⁷ + 210ρ⁵ − 60ρ³ + 5ρ)sin θ Z₃₆ 252ρ¹⁰ − 630ρ⁸ + 560ρ⁶ − 210ρ⁴ + 30ρ² − 1 Z₃₇ 924ρ¹² −2772ρ¹⁰ + 3150ρ⁸ − 1680ρ⁶ + 420ρ⁴ − 42ρ² + 1

In actual, the differential is detected as the above positionaldeviations, therefore, the fitting needs to be performed on thederivatives. In the polar coordinate system (x=ρ cos θ, y=ρ sin θ), theyare expressed as in the following equations (4) and (5).

$\begin{matrix}{\frac{\partial W}{\partial x} = {{\frac{\partial W}{\partial\rho}\cos\;\theta} - {\frac{1}{\rho}\frac{\partial W}{\partial\theta}\sin\;\theta}}} & (4) \\{\frac{\partial W}{\partial y} = {{\frac{\partial W}{\partial\rho}\sin\;\theta} + {\frac{1}{\rho}\frac{\partial W}{\partial\theta}\cos\;\theta}}} & (5)\end{matrix}$

Because the differential of the Zernike polynomial is not an orthogonalsystem, the fitting needs to be performed in the least squares method.The information on the image forming point of an spot image (thedeviation amount) is given for the X direction and the Y direction,therefore, when the number of pinholes is set as n (n is, for example,from around 81 up to 400), the number of the observation equations thatwill be given in the above equations (1) to (5) are 2n (from around 162up to 800).

Each term of the Zernike polynomial corresponds to an opticalaberration. Moreover, the low order terms (the terms whose value _(i) issmall) substantially corresponds to the Seidel aberrations. So, by usingthe Zernike polynomial, the wavefront aberration of projection opticalsystem PL can be obtained.

The calculation procedure of the conversion program is decided accordingto the principle described above, and by the calculation processaccording to the conversion program, the information on the wavefront(wavefront aberration) corresponding to each of the measurement pointsfrom the 1^(st) measurement point to the n^(th) measurement point withinthe field of projection optical system PL is obtained, which is in thiscase, the coefficients of each term of the Zernike polynomial, such asthe coefficient Z₁ of the 1^(st) term to the coefficient Z₃₇ of the37^(th) term.

Referring back to FIG. 1, inside the hard disc or the like that thefirst communications server 920 comprises, the target information to beachieved by the first to third exposure apparatus 922 ₁ to 922 ₃ isstored, such as the resolution, the practical minimum line width (thedevice rule), the wavelength of illumination light EL (such as centerwavelength and wavelength width), information on the patterns subject totransfer, and any other information that is related to determining thequality of the projection optical system of the exposure apparatus 922 ₁to 922 ₃ that may possibly be a target value. In addition, in the harddisc that the first communications server 920 comprises, the targetinformation of the exposure apparatus that is to be introduced, forexample, such as the information on the pattern that is planned to beused, is also stored as the target information.

Meanwhile, inside the storage unit such as the hard disc or the likethat the second communications server 930 comprises, an optimizingprogram is installed that optimizes the state of a projected image of apattern formed on an object under any targeted exposure conditions,along with the first database and the second database pertaining to theoptimizing program. That is, the optimizing program, the first database,and the second database are stored in an information storage media suchas a CD-ROM, which is inserted into a drive unit such as a CD-ROM drivethat the second communications server 930 comprises, and the optimizingprogram is installed into a storage unit such as a hard disc from thedrive unit, while the first database and the second database are copied.

The first database is a database of a wavefront aberration variationtable per each projection optical system (projection lens) that theexposure apparatus such as exposure apparatus 922 ₁ to 922 ₃ comprise.The wavefront aberration variation table, in this case, is a variationtable that can be obtained by performing simulation using a modelsubstantially equivalent to projection optical system PL, being composedof groups of data arranged according to a predetermined rule that showsthe relation between the change in a unit adjustment amount of anadjustment parameter that can be used to optimize the state of theprojected image of the pattern formed on the object that can beobtained, and the image forming quality corresponding to each of aplurality of measurement points within the field of projection opticalsystem PL, or to be more specific, wavefront data, such as the variationamount of the coefficients of the Zernike polynomial from the 1^(st)term to the 37^(th) term.

In the embodiment, as the above adjustment parameters, a total of 19parameters are used: z₁, θx₁, θy₁, z₂, θx₂, θy₂, z₃, θx₃, θy₃, z₄, θx₄,θy₄, z₅, θx₅, and θy₅, which are the drive amount of movable lenses 13₁, 13 ₂, 13 ₃, 13 ₄, and 13 ₅ in directions of each degree of freedom(drivable direction); Wz, Wθx, and Wθy, which are the drive amount ofthe surface of wafer W (Z tilt stage 58); and Δλ, which is the shiftamount of the wavelength of exposure light EL.

The procedure of making the database will now be briefly described.First of all, designed values of projection optical system PL (such asnumerical aperture (N.A.), coherence factor value σ, illumination lightwavelength λ, and data on each lens) is input into a simulation computerwhere specific optical software is installed. Next, data at any firstmeasurement point within the field of projection optical system PL isinput into the simulation computer.

Next, unit quantity data on the shift amount of movable lenses 13 ₁ to13 ₅ in directions of each degree of freedom (movable directions), thesurface of wafer W in the above degrees of freedom, and of theillumination wavelength is input. For example, when instructions areinput to drive movable lens 13 ₁ by only a unit quantity in a +direction in a Z direction shift, the simulation computer calculates thedata of a first wavefront from the ideal wavefront at a firstmeasurement point decided in advance within the field of projectionoptical system PL, such as the variation amount of the coefficients ofeach of the terms in the Zernike polynomial (for example, from the1^(st) term to the 37^(th) term), and the variation data is shown on thescreen of the simulation computer, as well as stored in memory asparameter PARA1P1.

Next, when instructions are input to drive movable lens 13 ₁ by a onlyunit quantity in a + direction in a Y direction tilt (rotation θx aroundthe X-axis), the simulation computer calculates the data of a secondwavefront at the first measurement point, such as the variation amountof the coefficients of the above terms in the Zernike polynomial, andthe variation data is shown on the above screen of the simulationcomputer, as well as stored in memory as parameter PARA2P1.

Then, when instructions are input to drive movable lens 13 ₁ by a onlyunit quantity in a + direction in an X direction tilt (rotation θyaround the Y-axis), the simulation computer calculates the data of athird wavefront at the first measurement point, such as the variationamount of the coefficients of the above terms in the Zernike polynomial,and the variation data is shown on the above screen of the simulationcomputer, as well as stored in memory as parameter PARA3P1.

Hereinafter, in the same procedure as in the above description, theinput for each measurement point from the 2^(nd) measurement point tothe n^(th) measurement point is performed, and each time instructionsare input to drive movable lens 13 ₁ in a Z direction shift, a Ydirection tilt, or an X direction tilt, the simulation computercalculates the data of a first, a second, and a third wavefront at eachmeasurement point, such as the variation of the coefficients of theabove terms in the Zernike polynomial, and the variation data is shownon the above screen of the simulation computer, as well as stored inmemory as parameters PARA1P2, PARA2P2, PARA3P2, . . . , PARA1Pn,PARA2Pn, PARA3Pn.

The input for each measurement point and instructions to drive themovable lens in by only a unit quantity in the +direction in directionsof each degree of freedom are performed also on other movable lenses 13₂, 13 ₃, 13 ₄, and 13 ₅, in the same procedure as in the abovedescription, and in response the simulation computer calculates the dataof the wavefront at each of the 1^(st) measurement point to the n^(th)measurement point for movable lenses 13 ₂, 13 ₃, 13 ₄, and 13 ₅, such asthe variation amount of the coefficients of the above terms in theZernike polynomial, and parameter (PARA4P1, PARA5P1, PARA6P1, . . . ,PARA15P1), parameter (PARA4P2, PARA5P2, PARA6P2, . . . , PARA15P2), . .. , parameter (PARA4Pn, PARA5Pn, PARA6Pn, . . . , PARA15Pn) are storedin memory.

In addition, input for each measurement point and instructions to drivewafer W by only a unit quantity in the + direction in directions of eachdegree of freedom are also performed in the same procedure as in theabove description, and in response the simulation computer calculatesthe data of the wavefront at each of the 1^(st) measurement point to then^(th) measurement point when wafer W is driven only by a unit quantityin directions of each degree of freedom, that is, in the Z, θx, and θydirections, such as the variation amount of the coefficients of theterms in the Zernike polynomial, and parameter (PARA16P1, PARA17P1,PARA18P1), parameter (PARA16P2, PARA17P2, PARA18P2), . . . , parameter(PARA16Pn, PARA17Pn, PARA18Pn) are stored in memory.

Furthermore, regarding wavelength shift, input for each measurementpoint and instructions to shift the wavelength by only a unit quantityin the + direction are also performed in the same procedure as in theabove description, and in response the simulation computer calculatesthe data of the wavefront at each of the 1^(st) measurement point to then^(th) measurement point when the wavelength is shifted in the +direction only by a unit quantity, such as the variation amount of thecoefficients of the terms in the Zernike polynomial, and PARA19P1,PARA19P2, . . . , and PARA19Pn are stored in memory.

Each of the above parameters PARAiPj (i=1 to 19, j=1 to n) is arow-matrix (vector) of 1 row and 37 columns. That is, when n=33, anadjustment parameter PARA1 can be expressed as in the followingequation, (6).

$\begin{matrix}\left. \begin{matrix}{{{PARA}\; 1P\; 1} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,37}\end{bmatrix}} \\{{{PARA}\; 1P\; 2} = \begin{bmatrix}Z_{2,1} & Z_{2,2} & \ldots & Z_{2,37}\end{bmatrix}} \\\vdots \\{{{PARA}\; 1P\; n} = \begin{bmatrix}Z_{33,1} & Z_{33,2} & \ldots & Z_{33,37}\end{bmatrix}}\end{matrix} \right\} & (6)\end{matrix}$

In addition, an adjustment parameter PARA2 can be expressed as in thefollowing equation, (7).

$\begin{matrix}\left. \begin{matrix}{{{PARA}\; 2P\; 1} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,37}\end{bmatrix}} \\{{{PARA}\; 2P\; 2} = \begin{bmatrix}Z_{2,1} & Z_{2,2} & \ldots & Z_{2,37}\end{bmatrix}} \\\vdots \\{{{PARA}\; 2P\; n} = \begin{bmatrix}Z_{33,1} & Z_{33,2} & \ldots & Z_{33,37}\end{bmatrix}}\end{matrix} \right\} & (7)\end{matrix}$

Similarly, the other adjustment parameters PARA3 to PARA19 can beexpressed as in the following equation, (8).

$\begin{matrix}\left. \begin{matrix}{{{PARA}\; 3P\; 1} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,37}\end{bmatrix}} \\{{{PARA}\; 3P\; 2} = \begin{bmatrix}Z_{2,1} & Z_{2,2} & \ldots & Z_{2,37}\end{bmatrix}} \\\vdots \\{{{PARA}\; 3P\; n} = \begin{bmatrix}Z_{33,1} & Z_{33,2} & \ldots & Z_{33,37}\end{bmatrix}} \\\vdots \\{{{PARA}\; 19P\; 1} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,37}\end{bmatrix}} \\{{{PARA}\; 19P\; 2} = \begin{bmatrix}Z_{2,1} & Z_{2,2} & \ldots & Z_{2,37}\end{bmatrix}} \\\vdots \\{{{PARA}\; 19P\; n} = \begin{bmatrix}Z_{33,1} & Z_{33,2} & \ldots & Z_{33,37}\end{bmatrix}}\end{matrix} \right\} & (8)\end{matrix}$

Then, PARA1P1 to PARA19Pn, which are composed of the variation amount ofthe coefficients of each of the Zernike polynomial and stored in memory,are grouped by each adjustment parameter and then sorted into awavefront aberration variation table for each of the 19 adjustmentparameters. That is, as is representatively shown in the followingequation, (9), in the case of adjustment data PARA1, a wavefrontaberration variation table is made for each parameter, which is storedin memory.

$\begin{matrix}{\begin{bmatrix}{{PARA}\; 1P\; 1} \\{{PARA}\; 1P\; 2} \\\vdots \\{{PARA}\; 1P\; n}\end{bmatrix} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,36} & Z_{1,37} \\Z_{2,1} & \; & \; & \; & Z_{2,37} \\\vdots & \; & ⋰ & \; & \vdots \\Z_{32,1} & \; & \; & \; & Z_{\;{32,\; 27}} \\Z_{33,1} & Z_{33,2} & \ldots & Z_{33,36} & Z_{33,37}\end{bmatrix}} & (9)\end{matrix}$

And, the database composed of the wavefront aberration variation tablefor each type of exposure apparatus made in the above manner is storedin the hard disc or the like that the second communications server 930comprises, as the first database. Although in the embodiment, onewavefront aberration variation table is made for the projection opticalsystem of the same type, the wavefront aberration variation table may bemade for each projection optical system (that is, per each exposureapparatus), regardless of the type.

Next, the second database will be described.

The second database is a database that includes the image formingquality of the projection optical system that is obtained underdifferent exposure conditions, which are optical conditions (such asexposure wavelength, numerical aperture (N.A.) of the projection opticalsystem (the maximum N.A, the N.A. set on exposure, or the like), andillumination conditions (illumination N.A (numerical aperture (N.A.) ofthe illumination optical system) or illumination σ (coherence factor),and the aperture shape of illumination system aperture stop plate 24(the light amount distribution of the illumination light on the pupilplane of the illumination optical system, that is, the shape of thesecondary light source)), and evaluation items (such as the type ofmask, line width, evaluation amount, and information on the pattern),and under a plurality of exposure conditions decided by combining suchoptical conditions and evaluation items, respectively. Such a databaseincluding the image forming quality of the projection optical system is,for example, a calculation chart made up of the variation amount of 1λin each of the 1^(st) to 37^(th) terms, or in other words, the ZernikeSensitivity Chart.

Incidentally, in the following description, the Zernike SensitivityChart will be referred to as Zernike Sensitivity or ZS. In addition, thefile composed of the Zernike Sensitivity Chart under a plurality ofexposure conditions will hereinafter be referred to as ‘ZS file’ asappropriate.

In the embodiment, each Zernike Sensitivity Chart contains the following12 aberrations as the image forming quality: that is, distortionsDis_(x) and Dis_(y) in the X-axis and Y-axis directions, four types ofline width abnormal values CM_(V), CM_(H), CM_(R), and CM_(L) that serveas index values for coma, four types of curvature of field CF_(V),CF_(H), CF_(R), and CF_(L), and two types of spherical aberration SA_(V)and SA_(H).

Next, the method of optimizing the state of the projected image of thereticle pattern formed on the wafer in the first to third exposureapparatus 922 ₁ to 922 ₃ will be described, according to a flow chart inFIG. 5 (and FIGS. 6 to 10 and 14 to 20), which is a processing algorithmof a processor that the second communications server 930 comprises.

The operation in the flow chart in FIG. 5 starts, for example, when anoperator of the exposure apparatus in the clean room sends instructionsthat include specifying the exposure apparatus subject to optimizing bye-mail via the first communications server 920 to an operator on theside of the second communications server 930, and the operator inputsinstructions to start the processing into the second communicationsserver 930.

First of all, in step 102, the screen to specify the equipment subjectto optimizing is shown on the display.

In the next step, step 104, the procedure is on standby until theequipment specified in the e-mail by the operator, such as exposureapparatus 922 ₁, is specified via a pointing device such as a mouse.Then, when the equipment is specified, the procedure proceeds onto step106, where the specified equipment is stored, for example, by storingdata such as the equipment number.

In the next step, step 108, the display shows the mode selecting screen.In the embodiment, a mode is selectable from modes 1 to 3, therefore,for example, the mode selecting screen shows selections buttons for mode1, mode 2, and mode 3.

In the next step, step 110, the procedure is on standby until the modeis selected. Then, when the operator selects the mode using the mouse orthe like, the step the proceeds to step 112 where the decision is madewhether the mode selected is mode 1 or not. When mode 1 is selected, thestep then proceeds to step 118, to a sub-routine that performsprocessing in mode 1 (hereinafter also referred to as ‘mode 1 processingroutine’). In this case, mode 1 is a mode where optimizing is performedusing an ID reference that is already available. Mode 1 is mainlyselected in cases when, for example, illumination conditions or thenumerical aperture (N.A.) of the projection optical system is changedduring the operation of exposure apparatus 922 ₁, in a state whereadjustment has already been performed under an exposure conditionserving as a reference (reference ID).

In mode 1 processing routine (hereinafter also referred to as ‘the firstmode’), first of all, in step 202 in FIG. 6, information on exposureconditions subject to optimizing (hereinafter referred to as ‘optimizingexposure conditions’ as appropriate) is obtained. To be more specific,an inquiry is made to the first communications server 920 (or to maincontroller 50 of the specified equipment (exposure apparatus 922 ₁) viathe first communications server 920) on setting information of thespecified equipment (exposure apparatus 922 ₁) such as the current N.Aof the projection optical system, illumination conditions (such asillumination N.A. or illumination σ, and the type of aperture stop), andthe subject pattern type, and the information obtained.

In the next step, step 204, an inquiry is made to the firstcommunications server 920 (or to main controller 50 of the specifiedequipment (exposure apparatus 922 ₁) via the first communications server920) on a reference ID that is the closest reference to the aboveoptimizing exposure conditions, and obtains the setting information suchas the N.A. of the projection optical system and illumination conditions(such as illumination N.A. or illumination σ, and the type of aperturestop) under the reference ID.

In the next step, step 206, necessary information on the stand-alonewavefront aberration and the above reference ID, or to be more specific,information on the adjustment amount values (adjustment parameters)under the reference ID, the wavefront aberration correction amountagainst the stand-alone wavefront aberration under the reference ID (orinformation on the image forming quality), or the like, is obtained fromthe first communications server 920 (or to main controller 50 of thespecified equipment (exposure apparatus 922 ₁) via the firstcommunications server 920).

The reason for referring to the wavefront aberration correction amount(or information on the image forming quality) here, is because when thewavefront aberration correction amount is unknown under the referenceID, the wavefront aberration correction amount (or the wavefrontaberration) can be estimated from the image forming quality. Theestimation of the wavefront aberration correction amount from the imageforming quality will be described later in the description.

Normally, the stand-alone wavefront aberration and the wavefrontaberration of projection optical system PL after it is built into theexposure apparatus (hereinafter referred to as ‘on-body wavefrontaberration’) do not coincide for some reason, however, for the sake ofsimplicity in the description, the correction is to be performed at thestart-up of the exposure apparatus or during the adjustment in themaking of the exposure apparatus for each of the reference IDs (theexposure condition serving as a reference).

In the next step, step 208, information on the apparatus such as thename of the model, its exposure wavelength, and the maximum N.A. of itsprojection optical system is obtained from the first communicationsserver 920 (or to main controller 50 of the specified equipment(exposure apparatus 922 ₁) via the first communications server 920).

Then, in the next step, step 210, the ZS file that corresponds to theoptimizing exposure conditions previously described, is searched for inthe second database.

In the next step, step 214, the decision is made whether the ZS filecorresponding to the optimizing exposure conditions has been found ornot, when it has been found, the ZS file is loaded into the memory suchas the RAM. On the other hand, when the decision in step 214 is denied,that is, when the ZS file corresponding to the optimizing conditions isnot available within the second database, the procedure then proceeds tostep 218 to make the ZS file using a ZS file in the second databaseaccording to, for example, an interpolation method that is describedbelow.

Following will be a brief description exemplifying such an interpolationmethod.

The Zernike Sensitivity (the Zernike Sensitivity Chart) changes,depending on the illumination conditions, the N.A. of the projectionoptical system, the type of reticle pattern, and the evaluation items.

As the illumination conditions, illumination σ and the light quantitydistribution of the illumination light on the pupil plane of theillumination optical system (for example, the size and shape of thesecondary light source referred to earlier) including the annular ratiocan be representatively given.

In addition, examples of the reticle pattern types include thefollowing: an extracted pattern or a residual pattern, a dense patternor an isolated pattern, in the case of dense lines (lines and spaces)its pitch, line width, and duty ratio, whereas in the case of isolatedlines its line width, in the case of contact holes its longitudinallength, its lateral length, and the length between the hole patterns(such as its pitch), and whether the reticle is a phase shift pattern(including a halftone type) or a phase shift reticle or not and its type(such as a spatial frequency modulation type and a halftone type).

In addition, the evaluation items include aberrations such asdistortion, the line width abnormal values (the index values for coma),focus (image plane), and spherical aberration (focus difference betweenpatterns); however, the evaluation items are not limited to the onesabove. For example, it may be of any other items, as long as it is animage forming quality (aberration) or its index value that can beevaluated using the Zernike polynomial.

In this interpolation method, basically, two or more known points arerequired that can be interpolated. Extrapolation will not be performed,because it causes some problems from the viewpoint of accuracy. Morespecifically, when there are only two known points, linear interpolationis performed. Whereas, when there are three or more known points, linearinterpolation or an interpolation with high precision such as polynomialapproximation (as in quadratic function or cubic function) or splineinterpolation is performed. The method to be employed is decideddepending on the amount of the Zernike Sensitivity variation ratio(first and second derivatives). When the variation is monotonous, linearinterpolation is performed.

In addition, when there is a plurality of conditions that are to beinterpolated, successive interpolation is performed.

Hereinafter, as an example, the case will be described when no ZS filesare available that coincide with the conditions of N.A. of theprojection optical system=0.74 and illumination σ (hereinafter alsoappropriately described as ‘σ’)=0.52 (however, conditions other than theN.A. and σ coincide with the required conditions), therefore, a ZS filerelated to focus is made by the interpolation method that contains theconditions of line width 100 nm, isolated lines, extracted pattern, N.A.of the projection optical system=0.74, and illumination σ=0.52. In thiscase, interpolation of the Zernike Sensitivity related to the pluralityof conditions N.A.=0.74 and illumination σ=0.52 needs to be sequentiallyperformed.

(1) First of all, the points that can be used for interpolation areconfirmed. That is, the ZS files that can be used for interpolation areselected. In the case of this example, because interpolation is to beperformed at three points, three points are selected for N.A. as well asfor σ, which makes 3×3=9 conditions of ZS files necessary. Then, the 9ZS files that can be interpolated are selected. That is, in this case, 9ZS files are selected whose N.A is 0.8, 0.7, or 0.6, and σ is 0.4, 0.5,or 0.6 as is shown below.ZS(N.A.=0.60, σ=0.4), ZS(N.A.=0.60, σ=0.5), ZS(N.A.=0.60, σ=0.6)ZS(N.A.=0.70, σ=0.4), ZS(N.A.=0.70, σ=0.5), ZS(N.A.=0.70, σ=0.6)ZS(N.A.=0.80, σ=0.4), ZS(N.A.=0.80, σ=0.5), ZS(N.A.=0.80, σ=0.6)

Hereinafter, interpolation calculation is performed in sequence for eachcondition.

(2) Interpolation calculation is performed to make the ZS file relatedto N.A.=0.74.

As is modeled in FIG. 11, in the vicinity of N.A.=0.74, when the ZernikeSensitivity related to N.A.=0.6, 0.7, and 0.8 is known, a quadricfunction approximation (or a spline interpolation) is performedaccording to the three points. As a result, the ZS files turn out to beas follows.

ZS(N.A.=0.6, σ=0.4), ZS(N.A.=0.6, σ=0.5), ZS(N.A.=0.6, σ=0.6)

ZS(N.A.=0.7, σ=0.4), ZS(N.A.=0.7, σ=0.5), ZS(N.A.=0.7, σ=0.6)

ZS(N.A.=0.74, σ=0.4), ZS(N.A.=0.74, σ=0.5), ZS(N.A.=0.74, σ=0.6)

ZS(N.A.=0.8, σ=0.4), ZS(N.A.=0.8, σ=0.5), ZS(N.A.=0.8, σ=0.6)

FIG. 11 shows the approximation curve of N.A.=0.74 obtained in thisinterpolation in a solid line C1.

(3) Next, interpolation calculation is performed to make the ZS filerelated to σ=0.52.

In the vicinity of σ=0.52, when the Zernike Sensitivity related toσ=0.4, 0.5, and 0.6 is known, a quadric function approximation (or aspline interpolation) is performed according to the three points. As aresult, the ZS files turn out to be as follows.

ZS(N.A.=0.6, σ=0.4), ZS(N.A.=0.6, σ=0.5), ZS(N.A.=0.6, σ=0.52),ZS(N.A.=0.6, σ=0.6)

ZS(N.A.=0.7, σ=0.4), ZS(N.A.=0.7, σ=0.5), ZS(N.A.=0.7, σ=0.52),ZS(N.A.=0.7, σ=0.6)

ZS(N.A.=0.74, σ=0.4), ZS(N.A.=0.74, σ=0.5), ZS(N.A.=0.74, σ=0.52),ZS(N.A.=0.74, σ=0.6)

ZS(N.A.=0.8, σ=0.4), ZS(N.A.=0.8, σ=0.5), ZS(N.A.=0.8, σ=0.52), ZS(N.A.=0.8, σ=0.6)

FIG. 11 shows the approximation curve of σ=0.52 obtained in thisinterpolation in a solid line C2.

As is obvious from FIG. 11, the intersecting point of the curves C1 andC2 (circled point (∘)) shows the ZS file related to focus made by theinterpolation method that contains the conditions of line width 100 nm,isolated lines, extracted pattern, N.A. of the projection opticalsystem=0.74, and illumination σ=0.52.

Employing the method of making a new ZS file by such an interpolationmethod easily solves realistic problems, such as the difficulty ofmaking all the ZS files in advance because of continuous variable itemssuch as the N.A and the σ, and the fact that the ZS files cannot be madeunder all conditions in a fine pitch in advance, due to too manycombinations.

In addition, the interpolation method has been confirmed suitable formaking new ZS files related to conditions such as the N.A. of theprojection optical system, illumination σ, annular ratio, pitch (denselines, contact holes), and longitudinal width/lateral width (contactholes). Furthermore, the above interpolation method is also effectivewhen making a ZS file related to the distance between a partial areawhere the intensity distribution of the illumination light on the pupilplane of the illumination optical system can be increased by modifiedillumination such as quadrupole illumination and the axis of theillumination optical system, or a ZS file related to the size of thepartial area (corresponding to illumination σ).

Next, in step 220 in FIG. 7, the display shows the specifying screen forspecifying the permissible value of the image forming quality (thetwelve aberrations referred to earlier). Then, in step 222, the decisionis made whether the permissible values are input or not, and when thedecision has been denied, the procedure then proceeds to step 226 wherethe decision is made to see if a certain period of time has elapsedafter the input screen for the above permissible values has beendisplayed. And, when the decision is negative, the procedure thenreturns to step 222. Meanwhile, in step 222, when the operator hasspecified the permissible values via the keyboard or the like, then thespecified permissible values for aberration are stored in memory such asthe RAM, and the procedure moves to step 226. That is, the procedurewaits for a certain period of time for the permissible values to bespecified, while steps 222→226 or steps 222→224→226 are being repeatedin a loop.

The permissible values do not necessarily have to be used in theoptimizing calculation itself (calculating the adjustment amount of theadjustment parameter using a merit function φ, which will be describedlater in the embodiment). They will, however, be required whenevaluating the calculation results. Furthermore, in the embodiment,these permissible values will be required when weighting of the imageforming quality is set, which will also be described later in thedescription.

Then, when the above certain period of time has elapsed, the procedurethen moves on to step 228 where the ZS database within the seconddatabase is read for permissible values of aberration that were notspecified are read, according to the default setting. As a consequence,both the specified permissible values of aberration and the remainingpermissible values read from the ZS database are stored in memory.

In the next step, step 230, the display shows a specifying screen forrestraint conditions, and then in step 232, the decision is made whetherthe restraint conditions have been input in step 232. When the decisionis denied, the procedure then moves to step 236 where the decision ismade to see if a certain period of time has passed since showing theabove specifying screen. When this decision is denied, the procedurethen returns to step 232. On the other hand, when the operator hasspecified the restraint conditions via the keyboard or the like in step232, the procedure then moves to step 234 where the restraint conditionsof the specified adjustment parameters are stored in memory such as theRAM, and then proceeds to step 236. That is, the procedure waits for acertain period of time for the permissible values to be specified, whilesteps 232→236 or steps 232→234→236 are being repeated in a loop.

Restraint conditions, in this case, refers to the permissible movablerange of each adjustment amount (adjustment parameter) referred toearlier such as the permissible movable range of movable lenses 13 ₁ to13 ₅ in directions of each degree of freedom, the permissible movablerange of Z tilt stage 58 in directions of three degrees of freedom, andthe permissible range of wavelength shift.

And, when the above certain period of time has elapsed, the procedurethen moves to step 238 where the movable range for each adjustmentparameter is calculated based on the current values as the restraintconditions of the parameters that were not specified, and is stored inmemory. As a consequence, both the restraint conditions of the specifiedadjustment parameters and the restraint conditions of the remainingadjustment parameters that have been calculated are stored in memory.

Next, in step 240 in FIG. 8, the display shows a screen to specify theweighting of the image forming quality. In the case of the embodiment,when specifying the weighting of the image forming quality, because the12 aberrations described earlier needs to be specified at 33 evaluationpoints (measurement points) within the field of the projection opticalsystem, 33×12=396 weightings need to be specified. Therefore, theweighting specifying screen is made to show the following two screens tospecify such weightings; first, the screen to specify the 12 types ofimage forming quality weighting, and then the screen to specify theweighting at each evaluation point within the field. In addition, on thescreen to specify the weighting of the image forming quality, anautomatic specify button is also shown.

Then, in step 242, the decision is made whether a weighting of an imageforming quality is specified or not. When the operator has specified aweighting via the keyboard or the like, the procedure then moves to step244 where the weighting of the specified image forming quality(aberration) is stored in memory such as the RAM, and then the procedureproceeds to step 248. In step 248, the decision is made whether acertain period of time has elapsed since the above weighting specifyingscreen has been displayed, and when the decision is negative, then theprocedure returns to step 242.

Meanwhile, when the decision turns out to be negative in the above step242, the procedure then moves to step 246 to see if the automaticspecify button has been selected. And, when the result is negative, theprocedure then moves to step 248. On the other hand, when the operatorhas selected the automatic specify button via the mouse or the like, theprocedure then moves to step 250 where the current image forming qualityis calculated based on the following equation, (10).f=Wa·ZS  (10)

In this case, f is an image forming quality expressed as in thefollowing equation (11), and Wa is the wavefront aberration data shownin the following equation (12), which is calculated from the stand-alonewavefront aberration and the wavefront aberration correction amountunder the reference ID obtained in step 206. In addition, ZS is data ofa ZS file, shown as in the following equation (13), which is obtained instep 216 or 218.

$\begin{matrix}{f = \begin{bmatrix}f_{1,1} & f_{1,2} & \ldots & f_{1,11} & f_{1,12} \\f_{2,1} & \; & \; & \; & f_{2,12} \\\vdots & \; & ⋰ & \; & \vdots \\f_{32,1} & \; & \; & \; & f_{\;{32,\; 12}} \\f_{33,1} & f_{33,2} & \ldots & f_{33,11} & f_{33,12}\end{bmatrix}} & (11) \\{{Wa} = \begin{bmatrix}Z_{1,1} & Z_{1,2} & \ldots & Z_{1,36} & Z_{1,37} \\Z_{2,1} & \; & \; & \; & Z_{2,37} \\\vdots & \; & ⋰ & \; & \vdots \\Z_{32,1} & \; & \; & \; & Z_{\;{32,\; 27}} \\Z_{33,1} & Z_{33,2} & \ldots & Z_{33,36} & Z_{33,37}\end{bmatrix}} & (12) \\{{ZS} = \begin{bmatrix}b_{1,1} & b_{1,2} & \ldots & b_{1,11} & b_{1,12} \\b_{2,1} & \; & \; & \; & b_{2,12} \\\vdots & \; & ⋰ & \; & \vdots \\b_{36,1} & \; & \; & \; & b_{\;{36,12}} \\b_{37,1} & b_{37,2} & \ldots & b_{37,11} & b_{37,12}\end{bmatrix}} & (13)\end{matrix}$

In equation (11), f_(i,1) (i=1 to 33) indicates Dis_(x) at the i^(th)measurement point, f_(i,2) indicates Dis_(y) at the i^(th) measurementpoint, f_(i,3) indicates CM_(V) at the i^(th) measurement point, f_(i,4)indicates CM_(H) at the i^(th) measurement point, f_(i,5) indicatesCM_(R) at the i^(th) measurement point, f_(i,6) indicates CM_(L) at thei^(th) measurement point, f_(i,7) indicates CF_(V) at the i^(th)measurement point, f_(i,8) indicates CF_(H) at the i^(th) measurementpoint, f_(i,9) indicates CF_(R) at the i^(th) measurement point,f_(i,10) indicates CF_(L) at the i^(th) measurement point, f_(i,11)indicates SA_(V) at the i^(th) measurement point, and f_(i,12) indicatesSA_(H) at the i^(th) measurement point, respectively.

In addition, in equation (12), Z_(i,j) indicates the coefficient of thej^(th) term in the Zernike polynomial.

In addition, in equation (13), b_(p/q) (p=1 to 37, q=1 to 12) indicatesthe components of the ZS file, and among the components, b_(p,1)indicates the change of Dis_(x) per 1λ in the p^(th) term of the Zernikepolynomial which is an expansion of the wavefront aberration, b_(p,2)indicates the change of Dis_(y) per 1λ in the p^(th) term, b_(p,3)indicates the change of CM_(V) per 1λ in the p^(th) term, b_(p,4)indicates the change of CM_(H) per 1λ in the p^(th) term, b_(p,5)indicates the change of CM_(R) per 1λ in the p^(th) term, b_(p,6)indicates the change of CM_(L) per 1λ in the p^(th) term, b_(p,7)indicates the change of CF_(V) per 1λ in the p^(th) term, b_(p,8)indicates the change of CF_(H) per 1λ in the p^(th) term, b_(p,9)indicates the change of CF_(R) per 1λ in the p^(th) term, b_(p,10)indicates the change of CF_(L) per 1λ in the p^(th) term, b_(p,11)indicates the change of SA_(V) per 1λ in the p^(th) term, and b_(p,12)indicates the change of SA_(H) per 1λ in the p^(th) term, respectively.

In the next step, step 252, of the calculated 12 types of image formingquality (aberrations), the weighting of the image forming quality thatgreatly exceeds the permissible values which are previously set isincreased (greater than 1), and then the procedure proceeds to step 254.This operation does not necessarily have to be performed, and the imageforming quality greatly exceeding the permissible values may be shown onthe screen in different colors instead. Such an arrangement helps theoperator when specifying the weighting of the image forming quality.

In the embodiment, the procedure waits for a certain period of time sothat the weighting of the image forming quality can be specified, whilethe loop composed of steps 242→246→248 or steps 242→244→248 is repeated.And when the automatic specify button is selected during the period,automatic specifying is performed. On the other hand, when the automaticspecify button is not selected, if at least one or more weighting of theimage forming quality is specified, the specified weighting is stored inmemory. Then, after a certain period of time, the procedure moves on tostep 253 where each weighting of the image forming quality that is notspecified is set to 1 according to a default setting, and then theprocedure proceeds to step 254.

As a consequence, both the specified weighting of the image formingquality and the remaining weighting (=1) are stored in memory.

In the next step, step 254, the display shows a screen for specifyingthe weighting at the evaluation points (measurement points) within thefield, and then in step 256 the decision is made whether the weightingat the evaluation points is specified or not. When the decision isnegative, the procedure then moves to step 260 where the decision ismade whether a certain period of time has elapsed or not since showingthe above screen for specifying the weighting at the evaluation points(measurement points). When the decision is negative, the procedurereturns to step 256.

Meanwhile, when the operator specifies the weighting of an evaluationpoint (normally, an evaluation point that especially needs to beimproved is selected) via the keyboard or the like in step 256, theprocedure then moves to step 258 where the weighting at the evaluationpoint is set and stored in memory such as the RAM. Then the proceduremoves on to step 260.

That is, the procedure waits for a certain period of time so that theweighting of the evaluation point can be specified, while the loopcomposed of steps 256→260 or steps 256→258→260 is repeated.

Then, after a certain period of time, the procedure moves on to step 262where the weighting of the evaluation points that is not specified areall set to 1 according to a default setting, and then the procedureproceeds to step 264.

As a consequence, both the specified value of the weighting at thespecified evaluation point and the weighting of the remaining evaluationpoints (=1) are stored in memory.

In step 264 in FIG. 9, the display shows the screen for specifying thetarget value (target) of the image forming quality (the 12 types ofaberrations referred to earlier) at each evaluation point in the field.In the case of the embodiment, the target of the image forming qualityneeds to be specified at 33 evaluation points (measurement points)within the field of the projection optical system for the 12 aberrationsdescribed earlier, so 33×12=396 targets need to be specified. Therefore,the screen for specifying the targets also shows a setting auxiliarybutton, along with the section for manual specification.

Then, in the next step, step 266, the procedure is suspended for apredetermined period of time to wait for the targets to be specified(that is, the decision is made whether the targets are specified ornot), and when they are not specified (when the decision is negative),the procedure moves to step 270 where the decision is made whether thesetting auxiliary button has been selected or not. When this decision isnegative, the procedure then proceeds to step 272 where the decision ismade whether a certain period of time has elapsed since the above targetspecifying screen has been displayed. And, when the decision isnegative, then the procedure returns to step 266.

Meanwhile, when the operator selects the setting auxiliary button withthe mouse or the like in step 270, the procedure then proceeds to step276 where an aberration decomposition method is performed.

The aberration decomposition method will now be described.

First of all, power expansion is performed on each image forming quality(aberration), which is a component of image forming quality f describedearlier, on x and y as in the following equation (14).f=G·A  (14)

In the above equation, (14), G is a 33 row 17 column matrix as is shownin the following equation (15).

$\begin{matrix}{G = \begin{bmatrix}{g_{1}\left( {x_{1},y_{1}} \right)} & {g_{2}\left( {x_{1},y_{1}} \right)} & \ldots & {g_{16}\left( {x_{1},y_{1}} \right)} & {g_{17}\left( {x_{1},y_{1}} \right)} \\{g_{1}\left( {x_{2},y_{2}} \right)} & \; & \; & \; & {g_{17}\left( {x_{2},y_{2}} \right)} \\\vdots & \; & ⋰ & \; & \vdots \\{g_{1}\left( {x_{32},y_{32}} \right)} & \; & \; & \; & {g_{17}\left( {x_{32},y_{32}} \right)} \\{g_{1}\left( {x_{33},y_{33}} \right)} & {g_{2}\left( {x_{33},y_{33}} \right)} & \ldots & {g_{16}\left( {x_{33},y_{33}} \right)} & {g_{17}\left( {x_{33},y_{33}} \right)}\end{bmatrix}} & (15)\end{matrix}$

In this case, g₁=1, g₂=x, g₃=y, g₄=x², g₅=xy, g₆=y², g₇=x³, g₈=x²y,g₉=xy², g₁₀=y³, g₁₁=x⁴, g₁₂=x³y, g₁₃=x²y², g₁₄=xy³, g₁₅=y⁴,g₁₆=x(x²+y²), and g₁₇=y(x²+y²). In addition, (x_(i), y_(i)) is the xycoordinate of the i^(th) evaluation point.

In addition, in the above equation (14), A is a matrix composed of 17rows and 12 columns whose components are decomposition coefficients, asis shown in the following equation (16).

$\begin{matrix}{A = \begin{bmatrix}a_{1,1} & a_{1,2} & \ldots & a_{1,11} & a_{1,12} \\a_{2,1} & \; & \; & \; & a_{2,12} \\\vdots & \; & ⋰ & \; & \vdots \\a_{16,1} & \; & \; & \; & a_{\;{16,12}} \\a_{17,1} & a_{17,2} & \ldots & a_{17,11} & a_{17,12}\end{bmatrix}} & (16)\end{matrix}$

The above equation (14) is then transformed into the following equation(17), so that the least squares method can be performed.G ^(T) ·f=G ^(T) ·G·A  (17)

In this case, G^(T) is a transposed matrix of matrix G.

Next, matrix A is obtained using a least squares method, based on theabove equation (17).A=(G ^(T) ·G)⁻¹ ·G ^(T) ·f  (18)

The aberration decomposition method is performed in the manner describedabove, and after the decomposition is completed, each of thedecomposition item coefficients is obtained.

Referring back to FIG. 9, in the next step, step 278, the display showseach of the decomposition item coefficients after decomposition obtainedin the manner described above, as well as the screen for specifying thetarget values of the coefficients.

Then, in the next step, step 280, the procedure is suspended to wait forall the target values (targets) of the decomposition item coefficientsto be specified. And, when the operator specifies all the targets of thedecomposition coefficients via the keyboard or the like, the step thenproceeds to step 282 where the targets of the decomposition itemcoefficients are converted into targets of the image forming quality. Inthis case, the operator specifies the target by revising the target onlyfor the coefficient that needs to be improved, and as for the remainingtargets, the coefficients shown may, as a matter of course, be specifiedas the targets.F _(t) =G·A′  (19)

In the above equation (19), f_(t) is a target of a specified imageforming quality, and A′ is a matrix whose component is the specifieddecomposition item coefficient (revised).

Incidentally, each of the decomposition item coefficients that iscalculated does not necessarily have to be shown on the screen, and thetarget that needs to be revised can be automatically set based on eachof the calculated decomposition item coefficients.

Meanwhile, when the operator specifies a target for an image formingquality at an evaluation point via the keyboard or the like in the abovestep 266, the decision made in step 266 is positive, and the proceduremoves on to step 268 where the specified target is set and stored inmemory such as the RAM. The procedure then moves on to step 272

That is, in the embodiment, the procedure waits for a certain period oftime from when the target specifying screen referred to earlier has beenshown so that the targets can be specified, while the loop composed ofsteps 266→270→272 or steps 266→268→272 is repeated. And, when thesetting auxiliary is specified during the period, the targets arespecified by calculating and showing the decomposition item coefficientsthat is calculated, and specifying the targets of the decomposition itemcoefficients, as is previously described. In the case the settingauxiliary button is not selected, when one or more image forming qualitytargets are specified at one or more evaluation points, the specifiedimage forming quality target at the evaluation point is stored inmemory. And, when a certain period of time elapses, the procedure thenmoves on to step 274 where each of the image forming quality targets ateach measurement point that were not specified are all set to 0according to a default setting, then the procedure proceeds to step 284.

As a result, both the specified image forming quality target at thespecified evaluation point and the remaining image forming qualitytargets (=0) are stored in memory, for example, in the form of a 33 row12 column matrix f_(t) as is shown in the following equation (20).

$\begin{matrix}{f_{t} = \begin{bmatrix}f_{1,1}^{\prime} & f_{1,2}^{\prime} & \ldots & f_{1,11}^{\prime} & f_{1,12}^{\prime} \\f_{2,1}^{\prime} & \; & \; & \; & f_{2,12}^{\prime} \\\vdots & \; & ⋰ & \; & \vdots \\f_{32,1}^{\prime} & \; & \; & \; & f_{32,12}^{\prime} \\f_{33,1}^{\prime} & f_{33,2}^{\prime} & \ldots & f_{33,11}^{\prime} & f_{33,12}^{\prime}\end{bmatrix}} & (20)\end{matrix}$

In the embodiment, the image forming quality at the evaluation pointswhere the targets are not specified is not taken into consideration inthe optimizing calculation. Accordingly, the image forming quality hasto be evaluated again, after the solutions are obtained.

In the next step, step 284, the display shows the screen for specifyingthe optimizing field range, and then the loop composed of steps 286→290is repeated while the procedure waits for a certain period of time forthe field range to be specified, after the specifying screen of theoptimizing field range is displayed. The reason for making it possibleto specify the optimizing range is because points such as the onesdescribed below are taken into consideration: in the scanning exposureapparatus such as in the so-called scanning steppers, the image formingquality or the transferred state of the pattern on the object in theentire field of the projection optical system does not necessarily haveto be optimized, or as in the case of steppers used in the embodiment,depending on the reticle that is used or its size of the pattern area(that is, the entire pattern area or a part of the pattern area that isused when exposing a wafer) the image forming quality or the transferredstate of the pattern on the object in the entire field of the projectionoptical system does not necessarily have to be optimized.

And, when the optimizing field is specified within a certain period oftime, the procedure then moves on to step 288 where the specified rangeis stored in memory such as the RAM. Then, the procedure proceeds tostep 294 in FIG. 294. On the other hand, when the optimizing field rangeis not specified, the procedure then simply proceeds to step 294 withoutperforming any particular operation.

In step 294, the current image forming quality is calculated, based onequation (10) referred to earlier.

Then, in the next step, step 296, an image forming quality variationtable is made for each adjustment parameter, using the wavefrontaberration variation table (refer to the equation (9) previouslydescribed) and the ZS (Zernike Sensitivity) file for each adjustmentparameter, or the Zernike Sensitivity Chart. This can be expressed as inthe following equation (21).image forming quality variation table=wavefront aberration variationtable·ZS file  (21)

The equation (21) is a calculation in which the wavefront aberrationvariation table (a matrix having 33 rows and 37 columns) and the ZS file(a matrix having 37 rows and 12 columns) are multiplied, therefore, theresults obtained, that is, an image forming quality variation table B1is, for example, a matrix that has 33 rows and 12 columns expressed asin the following equation (22).

$\begin{matrix}{{B\; 1} = \begin{bmatrix}h_{1,1} & h_{1,2} & \ldots & h_{1,11} & h_{1,12} \\h_{2,1} & \; & \; & \; & h_{2,12} \\\vdots & \; & ⋰ & \; & \vdots \\h_{32,1} & \; & \; & \; & h_{32,12} \\h_{33,1} & h_{33,2} & \ldots & h_{33,11} & h_{33,12}\end{bmatrix}} & (22)\end{matrix}$

The image forming quality variation table is calculated for each of the19 adjustment parameters. As a result, 19 image forming qualityvariation tables B1 to B19 are obtained, each composed of a matrixhaving 33 rows and 12 columns.

In the next step, step 298, image forming quality f and its target f_(t)are made into a single column (one-dimensional column). Being made intoa single column, in this case, means to transform the matrices f andf_(t) of 33 rows and 12 columns into matrices of 396 rows and a singlecolumn. The following equations (23) and (24) are f and f_(t), aftersuch transformation is performed.

$\begin{matrix}{f = \begin{bmatrix}f_{1,1} \\f_{2,1} \\\vdots \\f_{33,1} \\f_{1,2} \\f_{2,2} \\\vdots \\f_{33,2} \\\vdots \\f_{1,12} \\f_{2,12} \\\vdots \\f_{33,12}\end{bmatrix}} & (23) \\{f_{t} = \begin{bmatrix}f_{1,1}^{\prime} \\f_{2,1}^{\prime} \\\vdots \\f_{33,1}^{\prime} \\f_{1,2}^{\prime} \\f_{2,2}^{\prime} \\\vdots \\f_{33,2}^{\prime} \\\vdots \\f_{1,12}^{\prime} \\f_{2,12}^{\prime} \\\vdots \\f_{33,12}^{\prime}\end{bmatrix}} & (24)\end{matrix}$

In the next step, step 300, the 19 image forming quality variationtables for each adjustment parameter made in the above step 296 aretransformed into a two-dimensional form. In this case, such atransformation into a two-dimensional form refers to converting the formof the 19 types of image forming quality variation tables that are eachmade up of a 33 row 12 column matrix into a matrix having 396 rows and19 columns so that each column shows the image forming quality variationat each evaluation point against an adjustment parameter. An example ofan image forming quality variation table that has completed such atwo-dimensional transformation is shown as B in the following equation(25).

$\begin{matrix}{B = \begin{bmatrix}h_{1,1} & h_{1,1}^{2} & {\ldots\;} & {\ldots\;} & h_{1,1}^{19} \\h_{2,1} & \; & \; & \; & \vdots \\\vdots & \; & \; & \; & \; \\h_{33,1} & \; & \; & \; & \; \\h_{1,2} & \; & \mspace{11mu} & \; & \vdots \\h_{2,2} & \; & \; & \; & \; \\\vdots & \; & \; & \mspace{11mu} & \; \\h_{33,2} & \; & \; & \; & \; \\\vdots & \; & \; & \; & \vdots \\h_{1,12} & \; & \; & \; & \; \\\vdots & \; & \; & \mspace{11mu} & \vdots \\h_{33,12} & {h_{33,12}^{2}\;} & {\ldots\;} & {\;\ldots} & h_{33,12}^{19}\end{bmatrix}} & (25)\end{matrix}$

When the image forming quality variation table has undergone suchtwo-dimensional transformation in the manner described above, theprocedure then moves on to step 302, where the variation amount(adjustment amount) of the adjustment parameter is calculated withoutconsideration of the restraint conditions.

Hereinafter, the processing in step 302 will be described. When theweighting is not taken into consideration, a relation that is expressedas in the following equation (26) exists between image forming qualitytarget f_(t) that has been made into a single column, image formingquality f that has been made into a single column, image forming qualityvariation table B that has undergone two-dimensional transformation, andan adjustment amount dx of the adjustment parameter.(f _(t) −f)=B·dx  (26)

In this case, dx is a matrix having 19 rows and 1 column as is shown inthe following equation (27) whose components are the adjustment amountsof each adjustment parameter. In addition, (f_(t)−f) is a matrix thathas 396 rows and 1 column, as is shown in the following equation (28).

$\begin{matrix}{{dx} = \begin{bmatrix}{dx}_{1} \\{dx}_{2} \\{dx}_{3} \\{dx}_{4} \\\vdots \\{dx}_{19}\end{bmatrix}} & (27) \\{\left( {f_{t} - f} \right) = \begin{bmatrix}{f_{1,1}^{\prime} - f_{1,1}} \\{f_{2,1}^{\prime} - f_{2,1}} \\\vdots \\{f_{33,1}^{\prime} - f_{33,1}} \\{f_{1,2}^{\prime} - f_{1,2}} \\{f_{2,2}^{\prime} - f_{2,2}} \\\vdots \\{f_{33,2}^{\prime} - f_{33,2}} \\\vdots \\{f_{1,12}^{\prime} - f_{1,12}} \\{f_{2,12}^{\prime} - f_{2,12}} \\\vdots \\{f_{33,12}^{\prime} - f_{33,12}}\end{bmatrix}} & (28)\end{matrix}$

When the above equation (26) is solved by the least squares method, itcan be expressed as in the following equation.dx=(B ^(T) ·B)⁻¹ ·B ^(T)·(f _(t) −f)  (29)

In this case, B^(T) is a transposed matrix of image forming qualityvariation table B referred to earlier, and (B^(T)·B)⁻¹ is an inversematrix of (B^(T)·B).

However, the case is rare when the weighting is not specified (all theweightings=1). Therefore, normally, when the weighting is specified, amerit function φ as is shown in the following equation (30), whichserves as a weighting function, is solved using the least squaresmethod.φ=Σw·(f _(ti) −f _(i))²  (30)

In this case, f_(ti) is a component of f_(t), and f_(i) is a componentof f. When the above equation is transformed, it can be expressed asfollows.φ=Σ·(w _(i) ^(1/2) ·f _(ti) −w _(i) ^(1/2) ·f _(i))²  (31)

Accordingly, when w_(i) ^(1/2)·f_(i) is a new image forming quality(aberration) f_(i)′ and w_(i) ^(1/2)·f_(ti) a new target f_(ti)′, thenmerit function φ will be expressed as follows.φ=Σ·(f _(ti) ′−f _(i)′)²  (32)

Accordingly, the above equation (32) may be solved using the leastsquares method. However, in this case, the image forming qualityvariation table expressed as in the following equation has to be used.∂f _(i) ′/∂x _(j) =w _(i) ^(1/2) ·∂f _(i) /∂x _(j)  (33)

As is described, in step 302 the 19 components of dx, that is, theadjustment amounts of the 19 adjustment parameters PARA1 to PARA19 areobtained by the least squares method, without taking into considerationthe restraint conditions.

In the next step, step 303, by substituting the adjustment amounts ofthe 19 adjustment parameters that are obtained into, for example, theabove equation (26), each component of matrix f, that is, the 12 typesof aberration (image forming quality) at all the evaluation points arecalculated.

In the next step, step 304, the decision is made whether the abovecalculated 12 types of aberration at all the evaluation points is withinthe individual permissible values that are set in advance or not, andwhen the decision is negative, the procedure then returns to step 240referred to earlier. Then, by performing the processing after step 240,the target and weighting are set again, and the optimizing processperformed.

Meanwhile, when the decision in step 304 is affirmed, the procedure thenmoves on to step 306 where the decision is made whether the adjustmentamounts of the 19 adjustment parameters calculated in the above step 302fail to satisfy the restraint conditions that have been previously set(the decision making method will be described further later in thedescription). And, when the decision is affirmed, the procedure thenmoves on to step 308.

Hereinafter, the processing that is performed when the restraintconditions are violated will be described, including step 308.

The merit function on such violation of the restraint conditions can beexpressed, as in the following expression (34).φ=φ₁+φ₂  (34)

In the above equation, φ₁ is an ordinary merit function as is shown inequation (30), and φ₂ is a penalty function (restraint conditionsviolation amount). When the restraint conditions are expressed as g_(j)and the boundary values b_(j), φ₂ is to be a weighted squared sum of theboundary value violation amount (g_(j)−b_(j)), as in the followingequation (35).φ₂ =Σw _(j)′·(g _(j) −b _(j))²  (35)

The reason for φ₂ being a squared sum of the boundary value violationamount is because when φ₂ takes the form of a squared sum of theviolation amount, the following equation (36) can be solved for dx bythe least squares method.∂φ/∂X=∂φ ₁ /∂X+∂φ ₂ /∂X=0  (36)

That is, dx can be obtained as in the normal least squares method.

Next, concrete processing on violation of the restraint conditions willbe described

Restraint conditions are physically determined by the movable range ofeach of the three drive axes (piezoelectric elements) of the movablelenses 13 ₁ to 13 ₅ and the tilt (θx and θy) limit physically determinesthe restraint conditions.

The movable range in each axis can be expressed as in the followingequations (37a) to (37c), with z1, z2, and z3 indicating the position ofeach axis.z1a≦z1≦z1b  (37a)z2a≦z2≦z2b  (37b)z3a≦z3≦z3b  (37c)

In addition, the limit unique to tilt can be exemplified as in thefollowing equation (37d).(θx ² +θy ²)^(1/2)≦+40″  (37d)

The reason for choosing 40″ is for the following reason. When 40″ istransformed into radian,

$\begin{matrix}{40^{''} = {{40/3600}\mspace{14mu}{degrees}}} \\{= {{\pi/\left( {90 \times 180} \right)}\mspace{11mu}{radian}}} \\{= {1.93925 \times 10^{- 4}{{radian}.}}}\end{matrix}$

Accordingly, for example, when a radius r of movable lenses 13 ₁ to 13 ₅is around 200 mm, the movement amount of each axis is as follows.

$\begin{matrix}{{{axis}\mspace{14mu}{movement}\mspace{14mu}{amount}} = {1.93925 \times 10^{- 4} \times 200\mspace{14mu}{mm}}} \\{= {0.03878\mspace{14mu}{mm}}} \\{= {{38.78\mspace{14mu} µ\; m} \approx {40\mspace{14mu} µ\; m}}}\end{matrix}$That is, when the tilt is 40″, the perimeter moves around 40 μm from thehorizontal position. The movement amount of each axis is strokes whoseaverage is around 200 μm, therefore, compared with such strokes of theaxes around 200 μm, 40 μm is an amount that cannot be ignored. The tilt,however, is not limited to 40″, and can be set at any value accordingto, for example, the strokes of the drive axis. In addition, therestraint conditions may take into consideration not only the movablerange previously described and the tilt limit, but also the shift rangeof the wavelength of illumination light EL or the movable range relatedto the wafer (Z tilt stage 58) in the Z direction and its tilt.

In order to prevent violation of the restraint conditions, the aboveequations (37a) to (37d) have to be satisfied at the same time.

Therefore, first of all, as is described in the above step 302,optimizing is performed without taking the restraint conditions intoconsideration, and the adjustment amount dx of the adjustment parametersis obtained. This dx is to be shown as a movement vector k0 (Zi, θx_(i),θy_(i), i=1 to 7) as in the diagram in FIG. 12. In this case, i=1 to 5correspond to movable lenses 13 ₁ to 13 ₅, i=6 corresponds to the wafer(Z tilt stage), and i=7 corresponds to the wavelength shift of theillumination light. The wavelength of the illumination light does notactually have three degrees of freedom, however, in this case, it does,for the sake of convenience.

Next, the decision is made whether at least one of the above conditions(37a) to (37d) is not satisfied (step 306), and when the decision isdenied, that is, the above equations (37a) to (37d) are all satisfied atthe same time, the processing when the restraint conditions are violatedwill not be required, therefore, the processing performed on violationof the restraint conditions comes to an end (steps 306→310). On theother hand, when at least one of the conditions in the above equations(37a) to (37d) is not satisfied, the procedure then moves on to step308.

In step 308, as is shown in FIG. 12, the movement vector k0 that hasbeen obtained is scaled down, and the condition and the point thatfirstly violate the restraint conditions are obtained. The vector isexpressed as k1.

Next, the optimizing calculation is reperformed, with the conditionserving as a restraint condition and the restraint condition violationamount regarded as an aberration. In this case, the image formingquality variation table related to the restraint condition violationamount is calculated at a point on k1. And, in this manner, movementvector k2 in FIG. 12 is obtained.

‘The restraint condition violation amount regarded as an aberration,’ inthis case, means that the restraint condition violation amount, whichcan be expressed as, for example, z1−z1 b, z2−z2 b, z3−z3 b,(θx²+θy²)^(1/2)−40, can be a restraint condition aberration.

For example, when z2 violates the restraint condition of z2≦z2 b, therestraint condition violation amount (z2−z2 b) can be regarded as anaberration and the normal optimizing processing can be performed.Accordingly, in this case, a row on the restraint condition is added tothe image forming quality variation table. Such restraint condition isadded also to the image forming quality (aberration) and its target. Inthis case, when the weighting is largely set, then z2 is consequentlyfixed to a boundary value z2 b.

Because the restraint condition is a nonlinear function of θx and θy, adifferent derivative can be obtained depending on the place picked forthe image forming quality variation table. Accordingly, the adjustmentamount (movement amount) and the image forming quality variation tablehave to be sequentially calculated.

Next, as is shown in FIG. 12, scaling is performed on vector k2, and thecondition and the point that firstly violate the restraint conditionsare obtained. Then, the vector up to the point is to be k3.

Hereinafter, the above setting of the restraint conditions issequentially performed (adding restraint conditions in the order of themovement vector violating the restraint conditions), and the processingfor re-optimizing and obtaining the movement amount (adjustment amount)is repeated until the restraint conditions are not violated.

With such operation, the following equation can be obtained as aconclusive movement vector.k=k1+k3+k5+  (38)

In this case, to simplify the process, k1 may be the solution (answer),that is, linear approximation may be performed. Or, when the optimalvalue is strictly searched within the range of the restraint conditions,k of the above equation (38) may be obtained by sequential calculation.

Next, optimizing that takes the restraint conditions into considerationis further described.

As is described, normally, the following equation stands.(f _(t) −f)=B·dx  (26)

By solving this equation using the least squares method, adjustmentamount dx of the adjustment parameter can be obtained.

The image forming quality variation chart can therefore be divided as isshown in the following equation (39), into a normal variation table anda restraint condition variation table.

$\begin{matrix}{B = \begin{bmatrix}B_{1} \\B_{2}\end{bmatrix}} & (39)\end{matrix}$

In this case, B₁ is a normal variation table without dependence onlocation. Meanwhile, B₂ is a restraint condition variation table that isdependent on location.

In addition, the left side of the above equation (26) (f_(t)−f) can alsobe divided into 2 accordingly, as is shown in the following equation(40).

$\begin{matrix}{{f_{t} - f} = \begin{bmatrix}{f_{t\; 1} - f_{1}} \\{f_{t\; 2} - f_{2}}\end{bmatrix}} & (40)\end{matrix}$

In this case, f_(t1) is the normal aberration target and f₁ is thecurrent aberration. In addition, f_(t2) is the restraint condition andf₂ is the current restraint condition violation amount.

Because restraint condition variation table B₂, current aberration f₁,and current restraint condition violation amount f₂ are dependent onlocation, they need to be newly calculated per movement vector.

Then, by performing optimizing calculations in the usual manner usingthe variation table, optimizing that takes the restraint conditions intoaccount is performed.

In step 308, the adjustment amount is obtained in the manner describedabove, taking the restraint conditions into account into consideration,and then the procedure returns to step 303.

On the other hand, when the decision in step 306 is denied, that is,when there is no restraint condition violation and when the restraintcondition violation has been dissolved, the procedure then moves on tostep 310 where the results are shown on the display. In the embodiment,the following are shown as results: the adjustment amount of 19adjustment parameters (in this case, the variation amount from theposition under the reference ID), the values of each adjustmentparameter after adjustment, the image forming quality (the 12 types ofaberration) values after optimizing, the wavefront aberration correctionamount (carrying over the same value as the wavefront aberrationcorrection amount under the reference ID), the OK button, and the NGbutton.

And, when the operator sees the results shown on the display and selectsthe NG button with the mouse or the like, the procedure then returns tostep 240 previously described. The NG button can be selected in casessuch as when the operator is satisfied with the weighting and the targetpermissible values that have been set, but wants to further improve aspecific aberration or the image forming quality at a specificevaluation point by resetting the weighting and performing theoptimizing again.

Meanwhile, when the operator sees the results shown on the display andselects the OK button with the mouse or the like, the procedure thenmoves on to step 314 where based on the calculated adjustment amount,each section that requires adjustment (at least one of movable lenses 13₁ to 13 ₅, the Z position and tilt of wafer W, and the wavelength shiftamount of the illumination light) is controlled via the firstcommunications server 920 and main controller 50 of exposure apparatus922 ₁.

In this case, as the adjustment amount of movable lens 13 i (i=1 to 5),when the displacement amount is calculated in directions of threedegrees of freedom, in the Z, θx (rotation around the x-axis), and θy(rotation around the y-axis) directions, these adjustment amounts aretransformed into drive amounts z1, z2, and z3 for each axis in thefollowing manner.

FIG. 13 shows the arrangement of a drive axis of movable lens 13 _(i).From the geometrical relation shown in this drawing, in order totransform Z, θx, and θy into drive amounts z1, z2, and z3 for each axis(#1, #2, and #3), it is obvious that the following equations (41a) to(41c) need to be calculated.z1=Z−r×tan θx  (41a)z2=Z+0.5×r×tan θx+r×cos 30°×tan θy  (41b)z3=Z+0.5×r×tan θx−r×cos 30°×tan θy  (41c)

That is, based on the above transformation results, for example, thesecond communications server 930 provides instruction values to imageforming quality correction controller 48 for driving movable lenses 13 ₁to 13 ₅ in directions of each degree of freedom. With these values,image forming quality correction controller 48 controls the appliedvoltage to each drive element driving the movable lenses 13 ₁ to 13 ₅ indirections of each degrees of freedom.

In the embodiment, the adjustment parameter referred to earlier includesdrive amount Wz, Wθx, and Wθy of wafer W and the wavelength shift amountΔλ of illumination light EL, and the adjustment amount corresponding tothese four adjustment parameters are calculated in advance. Theadjustment amount of these four adjustment parameters, which is made tocorrespond to the optimizing exposure conditions (including illuminationconditions) referred to earlier, is stored in memory, and when a patternis transferred onto the wafer under such exposure conditions it is readand used. That is, the adjustment amount of the three adjustmentparameters related to the wafer is used in the focus leveling control ofthe wafer that uses the focus detection system previously described, andthe adjustment amount of the parameter related to the wavelength of theillumination light is used when setting the center wavelength of theillumination light in light source 16. In addition, the adjustmentamount of the movable lenses and their drive amount can also be made tocorrespond with the to the optimizing exposure conditions referred toearlier and stored in memory, and when a pattern is transferred onto thewafer under such exposure conditions it can be read form the memory andused to drive the movable lenses.

By controlling each of the above adjustment portions, exposure apparatus922 ₁ is optimized, which optimizes the forming state of the projectedimage of the reticle pattern on wafer W on exposure.

Then, the processing routine of the first mode (mode 1) is completed,and the procedure then returns to step 122 of the main routine in FIG.5.

Meanwhile, in the above step 110, when the operator selects mode 2 witha mouse or the like, the decision in step 114 turns out to be positive,and the procedure then moves on to step 116 where a subroutine thatperforms the mode 2 processing (hereinafter also referred to as ‘mode 2processing routine’) is performed. In this case, mode 2 is a mode inwhich optimizing is performed based on actual measurement data ofwavefront aberration (or image forming quality) under optional exposureconditions (optional IDs). Mode 2 is mainly selected when adding newIDs. While using exposure apparatus 922 ₁ in a state where each of theabove adjustment portions referred to earlier are adjusted according tothe optimizing results in mode 1, when a service technician measures thewavefront aberration of the projection system at times such asmaintenance, errors in the calculated adjustment amount according tomode 1 can consequently be corrected by performing the processing inmode 2 that will be described in the description below.

When mode 2 is selected, as a premise, the wavefront aberration ofprojection optical system PL of the subject equipment is to be measuredunder the current ID (the ID subject to optimizing). Accordingly, inthis case, information that the wavefront aberration has been measuredis also to be sent by e-mail or the like referred to earlier, along withthe specification of the exposure apparatus (equipment) subject tooptimizing and instructions to perform optimizing.

In the processing routine in mode 2 (hereinafter also referred to as‘the second mode’), first of all, in step 402 in FIG. 14, information onexposure conditions subject to optimizing is obtained. To be morespecific, an inquiry is made to the first communications server 920 (orto main controller 50 of the specified equipment (exposure apparatus 922₁) via the first communications server 920) and obtains settinginformation such as, the current N.A of the projection optical system,illumination conditions (such as illumination N.A., illumination σ, andthe types of aperture stops), and the types of subject patterns.

In the next step, step 406, measurement data on the new wavefront(coefficients of each term in the Zernike polynomial that expand thewavefront corresponding to the 1^(st) measurement point to the n^(th)measurement point, such as coefficient Z₁ of the first term tocoefficient Z₃₇ of the 37^(th) term) and necessary relative informationis obtained by communications, or to be more specific, the values of theadjustment amount (adjustment parameter) on measurement of the wavefrontaberration. Such values of the adjustment amount, that is, thepositional information of movable lenses 13 ₁ to 13 ₅ in directions ofthree degrees of freedom or the like normally coincides with the valuesat this point, that is, the values under the exposure conditions subjectto optimizing.

In the next step, step 408, in a manner similar to the one describedearlier in step 208, information on the apparatus such as the name ofthe model, its exposure wavelength, and the maximum N.A. of itsprojection optical system is obtained.

In the next step, step 410, as is previously described in step 210, theZS file that corresponds to the optimizing exposure conditions issearched for in the second database.

And, in steps 414, 416, and 418, processing (that includes decisionmaking) similar to the one performed in steps 214, 216, and 218previously described is performed. With this operation, when the ZS filethat corresponds to the optimizing exposure conditions is found withinthe second database, it is read into memory, whereas, when it cannot befound, then the ZS file is made by the interpolation method, which isdescribed earlier in the description.

Next, in steps 420 to 438 in FIG. 15, processing (that includes decisionmaking) similar to the one performed in steps 220 to 238 previouslydescribed is performed. With this operation, the permissible values ofthe image forming quality and restraint conditions of the adjustmentamount are set.

Next, in steps 440 to 462 in FIG. 16, processing (that includes decisionmaking) similar to the one performed in steps 240 to 262 previouslydescribed is performed. With this operation, weighting of the 12 typesof aberration at the 33 evaluation points (measurement points) withinthe field of the projection optical system is set in a manner similar tothe one described earlier in the description. However, in the secondmode processing, when automatic selection is selected in step 446, thenthe procedure moves on to step 450 where the present image formingquality is calculated based on the following equation (42).f=Wa′·ZS  (42)

In this case, f is the image forming quality expressed in equation (11)referred to earlier, and ZS is the ZS file data shown in the previousequation (13), which is obtained in step 416 or 418. In addition, Wa′ isthe wavefront aberration data (actual measurement data) obtained in step406, shown as in the following equation (43). That is, in the secondmode, the point where it uses actual measurement data when calculatingthe image forming quality differs from the first mode (mode 1).

$\begin{matrix}{{Wa}^{\prime} = \begin{bmatrix}Z_{1,1}^{\prime} & Z_{1,2}^{\prime} & \ldots & Z_{1,36}^{\prime} & Z_{1,37}^{\prime} \\Z_{2,1}^{\prime} & \; & \; & \; & Z_{2,37}^{\prime} \\\vdots & \; & {\; ⋰} & \; & \vdots \\Z_{32,1}^{\prime} & \; & \; & \; & Z_{32,37}^{\prime} \\Z_{33,1}^{\prime} & Z_{33,2}^{\prime} & \ldots & Z_{33,36}^{\prime} & Z_{33,37}^{\prime}\end{bmatrix}} & (43)\end{matrix}$

In the above equation (43), Z_(i,j)′ shows the j^(th) coefficient (j=1to 37) in the Zernike polynomial of the wavefront aberration at thei^(th) measurement point.

Next, in steps 464 to 490 in FIG. 17, processing (that includes decisionmaking) similar to the one performed in steps 264 to 290 previouslydescribed is performed. With this operation, the target values (targets)of the 12 types of aberrations at the 33 evaluation points within thefield of the projection optical system is set, as well as the optimizingfield range when the range is specified. In the mode 2 processing,however, when the setting auxiliary is specified (selected) in step 470,the aberration decomposition method is performed in step 476. In thiscase, image forming quality f calculated by the above equation (42) isused.

Next, in step 494 in FIG. 18, the present image forming quality iscalculated, based on equation (42) previously described.

In the next step, step 496, the image forming quality variation tablefor each adjustment parameter is made, similar to step 296 previouslydescribed.

In the next step, step 498, image forming quality f calculated in step494 and its target f_(t) are made into a single column (one-dimensionalcolumn).

Next, in step 500, the 19 image forming quality variation tables aretransformed into a two-dimensional form as in step 300 previouslydescribed, then the procedure moves on to step 502 where the variationamount (adjustment amount) of the adjustment parameter is calculatedwithout consideration of the restraint conditions, as in step 302referred to earlier.

In the next step, step 503, by substituting the adjustment amounts ofthe 19 adjustment parameters that are obtained into, for example, theabove equation (26), each component of matrix f, that is, the 12 typesof aberration (image forming quality) at all the evaluation points arecalculated.

In the next step, step 504, the decision is made whether the abovecalculated 12 types of aberration at all the evaluation points is withinthe individual permissible values that are set in advance or not, andwhen the decision is negative, the procedure then returns to step 440referred to earlier. Then, by performing the processing after step 440,the target and weighting are set again, and the optimizing processperformed.

Meanwhile, when the decision in step 504 is affirmed, the procedure thenmoves on to step 506 where the decision is made whether the adjustmentamounts of the 19 adjustment parameters calculated in the above step 502fail to satisfy the restraint conditions that have been previously set(the decision making method will be described further later in thedescription). And, when the decision is affirmed, the procedure thenmoves on to step 508 where optimizing is re-performed by sequentiallysetting the restraint conditions in consideration of the restraintconditions and the adjustment amount is obtained, as in step 308, andthen the procedure returns to step 503.

On the other hand, when the decision in step 506 is denied, that is,when there is no restraint condition violation and when the restraintcondition violation has been dissolved, the procedure then moves on tostep 510 where the results are shown on the display. In the embodiment,the following are shown as results: the adjustment amount of 19adjustment parameters (in this case, the variation amount from thedefault values), the values of each adjustment parameter afteradjustment, the image forming quality (the 12 types of aberration)values after optimizing, the wavefront aberration correction amount, theOK button, and the NG button.

And, when the operator sees the results shown on the display and selectsthe NG button with the mouse or the like, the procedure then returns tostep 440.

Meanwhile, when the operator sees the results shown on the display andselects the OK button with the mouse or the like, the procedure thenmoves on to step 514 where based on the calculated adjustment amount,each section that requires adjustment (at least one of movable lenses 13₁ to 13 ₅, the Z position and tilt of wafer W, and the wavelength shiftamount of the illumination light) is controlled via the firstcommunications server 920 and main controller 50 of exposure apparatus922 ₁, in a manner similar to the one previously described. Bycontrolling each of the above adjustment portions, exposure apparatus922 ₁ is optimized, which optimizes the forming state of the projectedimage of the reticle pattern on wafer W on exposure.

Then, the processing routine of the second mode (mode 2) is completed,and the procedure then returns to step 122 of the main routine in FIG.5.

Furthermore, when the operator selects mode 3 with the mouse or the likein the above step 110, the decision made in step 114 turns out negative,and the procedure moves on to step 120 where the sub-routine ofprocessing in mode 3 (hereinafter also referred to as ‘mode 3 processingroutine’) is performed. Mode 3, in this case, is a mode in which theimage forming quality (in the case of the embodiment, the 12 types ofaberration) is obtained under any exposure condition (optional ID), in astate where the wavefront aberration is known in a reference state andthe values of the adjustment parameters are fixed at that point. Mode 3can be suitably used, not only by device manufacturers but also byexposure apparatus makers during the making stage of the apparatus toadjust the optical properties of the projection optical system, so thatthe image forming quality improves and nears the desired target value.

In mode 3 processing routine (hereinafter also referred to as ‘the thirdmode’), first of all, in step 602 in FIG. 19, the adjustment amountvalues (adjustment parameters), the stand-alone wavefront aberration,and the wavefront aberration correction amount against the stand-alonewavefront aberration are obtained under the current state from the firstcommunications server 920 (or to main controller 50 of the specifiedequipment (exposure apparatus 922 ₁) via the first communications server920). The information obtained will be information of mode 3 in areference state.

In the next step, step 604, information on the apparatus such as thename of the model, its exposure wavelength, and the maximum N.A. of itsprojection optical system is obtained from the first communicationsserver 920 (or to main controller 50 of the specified equipment(exposure apparatus 922 ₁) via the first communications server 920).

In the next step, step 606, the display shows an input screen forinputting information on the subject pattern. And then, the procedureproceeds to step 608 where it waits for information on the subjectpattern to be input.

And, when the operator inputs information on the subject pattern (suchas whether the pattern is an extracted pattern or a residual pattern, adense pattern or an isolated pattern, in the case of dense lines (linesand spaces) its pitch, line width, and duty ratio, in the case ofisolated lines its line width, in the case of contact holes itslongitudinal length, its lateral length, and the length between the holepatterns (such as its pitch), and whether the reticle pattern type is aphase shift pattern (including a halftone type) or a phase shift reticleor not and its type (such as a spatial frequency modulation type and ahalftone type) via the keyboard or the like, the procedure then moves onto step 610 where the information on the pattern that has been input isstored in memory such as the RAM.

In the next step, step 612, the display shows an input screen forinputting illumination conditions. And then, the procedure proceeds tostep 614 where it waits for information on illumination conditions to beinput. And, when the operator inputs information on illuminationconditions such as illumination N.A of the illumination optical systemor illumination σ, annular ratio, and the aperture shape of illuminationsystem aperture stop plate 24 (the shape of the secondary light source)via the keyboard or the like, in step 615 the illumination conditionsthat have been input are stored in memory such as the RAM.

In the next step, step 616, the display shows an input screen forinputting the N.A. of the projection optical system. Then, the procedureproceeds to step 617 where it waits for the N.A. to be input. And, whenthe operator inputs the N.A via the keyboard or the like, the procedurethen moves on to step 618 where the N.A. that has been input is storedin memory such as the RAM.

In the next step, step 619, the display shows a specifying screen forspecifying an aberration that is to be a target and is subject toevaluation of the image forming quality (hereinafter referred to as‘target aberration’ as appropriate). And then, the procedure thenproceeds to step 620 where the decision is made whether the targetaberration has been specified or not. On the specifying screen for thetarget aberration, a specifying complete button is also shown.

And, when the operator specifies an aberration from the 12 types ofaberration described earlier as the target aberration via the keyboardor the like, the specified target aberration is stored in memory such asthe RAM as the evaluation subject. Then, the procedure proceeds to step624 where the decision is made whether the specifying complete buttonhas been selected or not. And, when the decision turns out to benegative, the procedure then returns to step 620. Meanwhile, when thedecision in step 620 is negative, the procedure then moves on to step624.

That is, in the embodiment, the loop made up of steps 620→622→624 orsteps 620→624 is repeatedly performed until the target aberration hasbeen specified. And, when the operator selects the specifying completebutton via the mouse or the like, the procedure then proceeds to step626. Other than specifying the target aberration by direct input as isdescribed above, the target aberration (evaluation item) can also bespecified, for example, by selecting the ZS file for differentevaluation items corresponding to the same illumination conditions andN.A. of the projection optical system. When specifying the targetaberration, the target aberration (evaluation item) may also bespecified in plurals.

In step 626, the ZS file corresponding to the evaluation condition issearched for in the second database. Evaluation condition, in this case,refers to the condition subject to evaluation, that is, conditions forevaluating the image forming quality of the evaluation items (in thiscase, the target aberration specified in step 620 and stored in memoryin step 622) under the exposure conditions determined by the informationinput in the above steps 610, 615, and 618 (hereinafter referred to as‘target exposure conditions’ as appropriate).

In the next step, step 628, the decision is made whether the ZS filecorresponding to the evaluation condition has been found or not. Whenthe file has been found, the ZS file is read into memory such as theRAM. On the other hand, when the decision is negative in step 628, thatis, when the ZS file corresponding to the evaluation condition is notavailable in the second database, the procedure then moves on to step632 where the ZS file corresponding to the evaluation condition is madeusing the ZS database within the second database, by for example, theinterpolation method previously described.

In the next step, step 634, the image forming quality of the evaluationitems under the target exposure condition (in this case, the targetaberration specified in step 620 and stored in memory in step 622) iscalculated in the following manner.

That is, by substituting the wavefront aberration data obtained from theinformation in the above step 602 and the ZS file data read in the abovestep 630 or made in the above step 632 into equation (10) previouslydescribed, the image forming quality at each evaluation point within thefield is obtained.

Then, in the next step, step 636, the display shows the information onthe calculated image forming quality. On the display, the OK button andthe redo button are also shown with the information on the image formingquality.

By the above display of the image forming quality, the operator canacknowledge the image forming quality, which is the evaluation item,under the target exposure condition that have been specified byhim/herself.

The operator then confirms the display, and when the image formingquality is sufficiently satisfying under the target exposure condition,selects the OK button using the mouse or the like. With this operation,the processing routine of the third mode is completed, and the procedurethen returns to step 122 of the main routine in FIG. 5.

On the other hand, when the operator confirms the display and is notsatisfied with the image forming quality under the target exposurecondition, the operator then selects the redo button with the mouse orthe like so that the image forming quality under other target exposureconditions can be checked. With this operation, the procedure thenreturns to step 606 where it shows the input screen for patterninformation, and then the processing (including decision making) of step608 and after is repeatedly performed.

In the third mode, by repeatedly selecting the redo button so thatvarious exposure conditions are set as the target exposure condition andthe image forming quality is calculated and displayed, the operator caneasily decide the best exposure condition. That is, for example, whenthe specified information other than the pattern information input instep 608 is fixed, and the operator repeatedly selects the redo buttonwhile gradually changing the pattern information so that the aboveoperations of making (or selecting) the ZS file and calculating theimage forming quality (target aberration) are repeatedly performed, theoperator can sequentially confirming the calculation results in step 636shown on the display and find the pattern information in which the imageforming quality (target aberration) becomes minimum (or optimum), whichallows the optimal pattern to be decided as the best exposure condition.

Similarly, the redo button can be repeatedly selected to repeatedlyperform the operations of making (or selecting) the ZS file andcalculating the image forming quality (target aberration) while aspecific condition is gradually changed and the remaining specifiedinformation is fixed, and by sequentially confirming the calculationresults in step 636 shown on the display, the specific condition inwhich the image forming quality (target aberration) becomes minimum (oroptimum) can be found, and the optimal specific condition can be decidedas the best exposure condition.

Referring back to FIG. 5, in step 122, the display shows a selectingscreen of whether to end or to continue the processing. When thecontinue button is selected, the procedure then returns to step 102,whereas when the end button is selected, the series of processing in theroutine is completed.

As is referred to earlier in the description, in the first modeprocessing, a case may be considered when the wavefront aberrationcorrection amount under the reference ID is unknown. In this case, thewavefront aberration correction amount can be estimated from the imageforming quality. Following is a description of such a case.

The correction amount of the wavefront aberration will be estimated onthe assumption that the deviation of the stand-alone wavefrontaberration and the on-body wavefront aberration corresponds to anadjustment amount deviation Δx′ of adjustment parameters of movablelenses 13 ₁ to 13 ₅ or the like referred to earlier.

When the adjustment amount under the assumption that the stand-alonewavefront aberration coincides with the on-body wavefront aberration isexpressed as Δx, the correction amount of the adjustment amount as Δx′,the ZS file as ZS, the theoretical image forming quality (thetheoretical image forming quality when there is no deviation in theon-body wavefront aberration) under the reference ID as K₀, the actualimage forming quality under the reference ID as K₁, the wavefrontaberration variation table as H, the image forming quality variationtable as H′, the stand-alone wavefront aberration as Wp, and thewavefront aberration correction amount as ΔWp, the following 2 equations(44) and (45) are valid.K ₀ =ZS·(Wp+H·Δx)  (44)K ₁ =ZS·(Wp+H·(Δx+Δx′))  (45)

From these equations,K ₁ −K ₀ =ZS·H·Δx′=H′·Δx′.  (46)

When the above equation (46) is calculated by the least squares method,the correction amount Δx′ of the adjustment amount can be expressed asin the following equation (47).Δx′=(H′ ^(T) ·H′)⁻¹ ·H′ ^(T)·(K ₁ −K ₀)  (47)

In addition, correction amount ΔWp of the wavefront aberration can beexpressed as in the following equation (48).ΔWp=H·Δx′  (48)

Each reference ID will have a wavefront aberration correction amountΔWp.

In addition, the actual on-body wavefront aberration will be as in thefollowing equation (49).the actual on-body wavefront aberration=Wp+H·Δx+ΔWp  (49)

With the exposure apparatus 922 ₁ to 922 ₃ in the embodiment, whenmanufacturing semiconductor devices, reticle R for manufacturing devicesis mounted on reticle stage RST, and then preparatory operations such asreticle alignment and the so-called baseline measurement, and waferalignment like the EGA (Enhanced Global Alignment) are performed.

Details on preparatory operations such as the above reticle alignmentand baseline measurement are disclosed in, for example, Japanese PatentApplication Laid-open No. H04-324923 and the corresponding U.S. Pat. No.5,243,195. In addition, details on the following operation, EGA, aredisclosed in, Japanese Patent Application Laid-open No. S61-44429, andthe corresponding U.S. Pat. No. 4,780,617. As long as the national lawsin designated states or elected states, to which this internationalapplication is applied, permit, the disclosures of the above publicationand the above U.S. patent are incorporated herein by reference.

Then, based on the wafer alignment results, exposure based on thestep-and-repeat method is performed. Details on exposure operations willbe omitted, since they are the same as in a typical stepper.

Next, the making method of exposure apparatus PL, which is performedwhen making exposure apparatus 922 (922 ₁ to 922 ₃), will be described,according to a flowchart in FIG. 21 that shows the making process ofprojection optical system PL.

As a premise, a computer system that has the same configuration as theone shown in FIG. 1 is to be built in the factory of the exposureapparatus maker (to be referred to as ‘maker B’). Hereinafter, as thereferences for each component, the same references will be used as theone used when describing the computer system of device manufacturer Aearlier in the description. In addition, for the sake of convenience inthe description, the first communications server 920 is to be disposedat the place where projection optical system PL is made.

[Step 1]

In step 1, the following parts that structure projection optical systemPL are made according to design values based on a predetermined designlens data: lens elements each serving as an optical member, lens holdersthat hold each of the lenses, and a barrel that houses an optical unitmade up of the lens elements and the lens holders. That is, each lenselement is processed using a well-known lens processor from apredetermined optical material, so that the lens element has a radius ofcurvature and axial thickness according to predetermined design values.In addition, the lens holder that holds each lens and the barrel thathouses the optical unit made up of the lens elements and the lensholders are processed into shapes of a predetermined size, using awell-known metal processor or the like from predetermined holdingmaterials (such as stainless steel, brass, or ceramics).

[Step 2]

In step 2, the surface shape of the lens surface of each lens elementthat makes up projection optical system PL made in step 1 is measuredusing, for example, a Fizeau interferometer. As such an interferometer,a unit whose light source is an He—Ne gas laser that emits light havinga wavelength of 633 nm, an Ar laser that emits light having a wavelengthof 363 nm, or a harmonic of an Ar laser having the wavelength of 248 nmis used. The Fizeau interferometer can accurately obtain the shape ofthe surface subject to detection, which is a lens element surface, bymeasuring interference fringe that is formed when the reflection beamsfrom a reference surface formed on the surface of a condenser lensdisposed on the optical path and the lens element surface interfere witheach other, using a pick-up device such as a CCD. Obtaining the shape ofthe surface (lens surface) of an optical element such as a lens usingthe Fizeau interferometer is well known, and the details are disclosedin, for example, Japanese Patent Application Laid-open Nos. S62-126305and H06-185997.

The above measurement of the surface shape of the optical element usingthe Fizeau interferometer is performed on all the lens surfaces of thelens elements that make up projection optical system PL. Then, a workerinputs each measurement result into the first communications server 920via an input device such as a console or the like (not shown). Theinformation input is transmitted to the second communications server 930from the first communications server 920, and is stored in memory suchas the RAM or in a storage unit such as the hard disc in the secondcommunication server 930.

[Step 3]

When the measurement of the surface shape of all the lens surfaces ofthe lens elements that make up projection optical system PL has beencompleted in step 2, the optical unit that is processed and madeaccording to design values, or more specifically, a plurality of opticalunits consisting of the optical elements such as lenses and lens holdersthat hold the lenses are assembled. Among these optical units, aplurality of units, such as five, have movable lenses 13 ₁ to 13 ₅described earlier in the description, respectively, and as is alsodescribed earlier in the description, such optical units with movablelenses 13 ₁ to 13 ₅ use lens holders that have a double structure. Thatis, the lens holders that have a double structure each have an innerlens holder that holds movable lenses 13 ₁ to 13 ₅ and an outer lensholder that holds the inner lens holder, and the positional relationbetween the inner lens holder and the outer lens holder is adjustablewith a mechanical adjustment mechanism. In addition, on the lens holderhaving such a double structure, drive elements that are previouslydescribed are provided at predetermined positions.

Then, the plurality of optical units assembled in the manner describedabove is sequentially assembled into the barrel via the opening on theupper end, being dropped into the barrel with spacers in between. Then,the first optical unit that is dropped into the barrel is supported by aprojected portion formed on the lower end of the barrel via a spacer,and when all the optical units are housed inside the barrel, theassembly process is completed. In parallel with the assembly process,information related to spacing in between the optical surface of thelens elements (lens surfaces) is measured using a tool such as amicrometer, taking into consideration the thickness of the spacers alsohoused with the optical units inside the barrel. And, while alternatelyperforming the assembly operation and the measurement operation of theprojection optical system, the final spacing in between the opticalsurface of the lens elements (lens surfaces) of projection opticalsystem PL at the point where the assembly process in step 3 has beencompleted is obtained.

During each processing in the making of the projection optical systemincluding the assembly process, movable lenses 13 ₁ to 13 ₅ previouslydescribed are fixed at a neutral position. In addition, although it isomitted in the description, in the assembly process, pupil aperture stop15 is also assembled into the system.

The worker inputs the measurement results, which is related to thespacing in between the optical surface of the lens elements (lenssurfaces) of projection optical system PL at the point during the aboveassembly process or when the assembly has been completed, into the firstcommunications server 920 via an input device such as a console or thelike (not shown). The information that has been input is transmittedfrom the first communications server 920 to the second communicationsserver 930, and is stored in memory such as the RAM or in a storage unitsuch as the hard disc in the second communication server 930. In theabove assembly process, the optical units may be adjusted whennecessary.

When adjusting the optical unit, for example, the relative spacingbetween optical elements in the optical axis direction may be changed orthe optical elements can be inclined against the optical axis, via themechanical adjustment mechanism. In addition, the barrel may bestructured so that the tip of a screw, which is screwed to an internalscrew that penetrates the side surface of the barrel, is in contact withthe lens holder. And, by making the screw move using a tool such as ascrew driver, the lens holder may be shifted in a directionperpendicular to the optical axis so that eccentricity or the like isadjusted. Details on an adjustment mechanism for moving the lens holdersin five or more degrees of freedom in order to perform opticaladjustment on the projection optical system assembled in the mannerdescribed above are disclosed in, for example, Japanese PatentApplication Laid-open No. 2002-162549.

[Step 4]

Next, in step 4, the wavefront aberration of projection optical systemPL assembled in step 3 is measured.

To be more specific, projection optical system PL is to be attached tothe body of a large wavefront aberration measuring unit (not shown)(suchas the PMI referred to earlier), and the wavefront aberration measured.The measuring principle of the wavefront by the wavefront aberrationmeasuring unit is the same as wavefront aberration measuring instrument80 previously described, therefore, the details will be omitted.

As a result of the above wavefront aberration measurement, the wavefrontof the projection optical system is expanded and coefficient Z_(i) (i=1,2, . . . , 81) of each term in a Zernike polynomial (Fringe Zernikepolynomial) is obtained by the wavefront aberration measuring unit.Accordingly, by connecting the wavefront aberration measuring unit tothe second communications server 930, the above coefficient Z_(i) ofeach term in the Zernike polynomial will automatically be loaded intomemory such as the RAM (or into a storage unit such as the hard disc) ofthe second communications server 930. In the above description, thewavefront aberration measuring unit uses the terms up to the 81^(st)term in the Zernike polynomial. In this case, the high order componentof each aberration of projection optical system PL can also becalculated. However, the calculation may be performed up to the 37^(th)term, as in the case of the wavefront aberration measuring unitpreviously described, or it may be performed on the 82^(nd) term andover.

[Step 5]

In step 5, projection optical system PL is adjusted so that thewavefront aberration measured in step 4 becomes optimal.

First of all, prior to adjusting projection optical system PL, thesecond communications server 930 corrects an optical basic data storedin advance in memory and reproduces the optical data of projectionoptical system PL in the making process that has actually been built,based on information stored in memory, that is, the information onsurface shape of the optical elements obtained in the above step 2 andthe information on spacing between optical surfaces of the opticalelements obtained in the above assembling process in step 3. The opticaldata is used to calculate the adjustment amount of each optical element.

That is, within the hard disc of the second communications server 930,an adjustment basic data is stored in advance that is a calculation on arelation between a unit drive amount of each lens element in directionsof 6 degrees of freedom and a variation amount of coefficient Z_(i) ofeach term in the Zernike polynomial based on design values of theprojection optical system, sort of like the wavefront aberrationvariation table referred to earlier but expanding to include not onlythe movable lenses but also the immovable lenses. Then, the secondcommunications server 930 corrects the above adjustment basic dataaccording to a predetermined calculation, based on the above opticaldata obtained during the making process of projection optical system PL.

Then, the second communications server 930 performs a predeterminedcalculation using the corrected database and the wavefront aberrationmeasurement results, and calculates the adjustment amount (includingzero) of each lens element in directions of 6 degrees of freedom, thenshows the information on the adjustment amount on the display. At thesame time, the second communications server 930 transmits theinformation on the adjustment amount to the first communications server920. Then, the first communications server 920 shows the information onthe adjustment amount on the display.

According to the display, a technician (worker) adjusts each lenselement. As a result, projection optical system PL whose wavefrontaberration is optimal is made.

In order to perform simple reprocessing of the optical elements ofprojection optical system PL, when the wavefront aberration is measuredusing the wavefront measurement unit as is described above, theavailability and position of the optical element(s) that requirereprocessing can be specified based on the measurement results, and thereprocessing of the optical element and the readjustment of theremaining optical elements may be performed in parallel.

Next, the making method of exposure apparatus 922 will be described.

On the making of exposure apparatus 922, first of all, illuminationoptical system 12 that includes optical elements such as a plurality oflens elements and mirrors is assembled as a unit, as well as projectionoptical system PL in the manner above. In addition, the reticle stagesystem and the wafer stage system that are made up of various mechanicalcomponents are also assembled as units. And then, optical adjustment,mechanical adjustment, and electrical adjustment are performed so thateach unit has a desired level of performance as stand-alone units. Onthis adjustment, the adjustment of projection optical system PL isperformed in the manner described above.

Next, units such as illumination optical system 12 and projectionoptical system PL are assembled into the exposure apparatus main body.The reticle stage system and the wafer stage system are also attached tothe exposure apparatus main body, and then the wiring and piping areconnected.

Next, optical adjustment is further performed on illumination opticalsystem 12 and projection optical system PL. This is because the imageforming quality of these optical systems, especially that of projectionoptical system PL slightly changes from before being assembled into theexposure apparatus to after being assembled. In the embodiment, on theoptical adjustment performed after projection optical system PL has beenbuilt into the exposure apparatus, wavefront aberration measuringinstrument 80 previously described is attached onto Z tilt stage 58 andmeasurement of the wavefront aberration is performed in the mannerdescribed earlier. Then, the information for each measurement pointobtained as the measurement results of wavefront aberration is sentonline from main controller 50 of the exposure apparatus being built tosecond communications server 930, via the first communications server920. And then, in a manner similar to the adjustment performed whenmaking projection optical system PL described above, the adjustmentamount of each lens element is calculated in directions of 6 degrees offreedom, and the calculation results are shown on the display of theexposure apparatus via the first communications server 920.

Then, according to the display, the technician (worker) adjusts eachlens element. As a result, projection optical system PL is made thatsatisfies the decided configurations without fail.

The final adjustment of projection optical system PL in its making stagecan be performed by automatic adjustment by main controller 50 via imageforming quality correction controller 48, based on instructions from thesecond communications server 930. However, at the point when the makingof the exposure apparatus has been completed, each movable lens ispreferably maintained at a neutral position so that the drive strokes ofthe drive elements after the exposure apparatus has been delivered aresufficiently secured. In addition, the aberration that has not beencorrected at this stage, mainly high order aberration, may be decided asaberration that cannot be automatically corrected, therefore, theassembly of the lenses or the like is preferably readjusted in themanner described above.

When the desired quality cannot be obtained by the above readjustment,some lenses may have to be reprocessed or exchanged. In order toreprocess the optical elements of projection optical system PL easily,the wavefront aberration can be measured before assembling projectionoptical system PL into the exposure apparatus main body using thewavefront aberration measuring unit only for measuring the wavefrontaberration, and based on the measurement results the presence of theoptical element that requires reprocessing and its position can bespecified, and the reprocessing of the optical element and thereadjustment of the remaining optical elements may be performed inparallel.

In addition, the optical element may be exchanged per the opticalelement of projection optical system PL, or, when the projection opticalsystem has a plurality of barrels, it may be exchanged per barrel.Furthermore, in the reprocessing of the optical element, the surface maybe processed into an aspheric surface if necessary. Also, when adjustingprojection optical system PL, the adjustment may be made only on theposition of the optical element (including the spacing between opticalelements) and its inclination, or when the optical element is a lenselement, it eccentricity may be changed or it may be rotated with theoptical axis AX serving as the center. Furthermore, in order to correctthe aberration of projection optical system PL, especially thenon-rotational symmetric component, for example, the wavefrontaberration may be measured in a state where a plane-parallel plate isassembled into projection optical system PL. And based on themeasurement results, the surface of the plane-parallel platedisassembled from projection optical system PL may be processed, andthen the processed plane-parallel plate (aberration correcting plate)may be reassembled into projection optical system PL. With suchoperation, projection optical system PL can be easily adjusted, or theadjustment can be performed with higher precision. The wavefrontaberration may be measured with the aberration correcting plate fixed toprojection optical system PL, and based on the measurement results theaberration correction plate may be reprocessed or exchanged.

Then, overall adjustment (such as electrical adjustment and operationverification) is further performed. By such operations, exposureapparatus 922 in the embodiment that can transfer a pattern of reticle Ron wafer W with good precision using projection optical system PL whoseoptical properties have been adjusted with high precision can be made.The exposure apparatus is preferably built in a clean room where thetemperature and the degree of cleanliness are controlled.

As is obvious from the description so far, in the embodiment, movablelenses 13 ₁ to 13 ₅, Z tilt stage 58 and light source 16 constitute anadjustment section, and the position (or the variation amount) ofmovable lenses 13 ₁ to 13 ₅ and Z tilt stage 58 in the Z, θx, and θydirections and the shift amount of the wavelength of the illuminationlight make up the adjustment amount. And, the above adjustment section,drive elements that drive the movable lenses, wafer stage drive section56 that drives image forming quality correction controller 48 and Z tiltstage 58, and main controller 50 which controls image forming qualitycorrection controller 48, wafer stage drive section 56, and light source16 constitute an adjustment unit. However, the arrangement of theadjustment unit is not limited to this, and for example, the adjustmentsection may only include movable lenses 13 ₁ to 13 ₅. Even in such acase, the image forming quality (aberrations) of the projection opticalsystem can be adjusted.

In addition, in the description so far, the measurement of the wavefrontaberration performed at times such as the adjustment of projectionoptical system PL has been performed using wavefront aberrationmeasuring instrument 80, based on the aerial images formed via pinholesand projection optical system PL. However, the present invention is notlimited to this, and the wavefront aberration may be measured using ameasurement mask that has a special structure, which is disclosed in,for example, U.S. Pat. No. 5,978,085. In this method, a plurality ofmeasurement patterns on the mask is sequentially exposed on an objectvia pinholes that are individually provided and projection opticalsystem PL, while reference patterns on the mask are exposed on theobject via only the projection optical system without passing throughthe condenser lens and pinholes. Then, the positional deviation of eachof the resist images of the plurality of measurement patterns to theresist images of the reference patterns that are obtained from theexposure are measured, and the wavefront aberration is calculated by apredetermined calculation.

Furthermore, the wavefront aberration may be measured using a PDI (PointDiffraction Interferometer), such as the one disclosed in, for example,Japanese Patent Application Laid-open No. 2000-97617. In addition,methods such as a phase recovering method whose details are disclosedin, for example, Japanese Patent Application Laid-open No. H10-284368,and in U.S. Pat. No. 4,309,602, and a method that uses a halftone phaseshift mask whose details are disclosed in, for example, Japanese PatentApplication Laid-open No. 2000-146757, can also be used. Moreover, amethod that uses a beam that passes through a part within the pupil ofthe projection optical system can also be used, as is disclosed in, forexample, Japanese Patent Application Laid-open No. H10-170399, JenaReview 1991/1, pp 8-12 “Wavefront analysis of photolithographic lenses”Wolfgang Freitag et al., Applied Optics Vol. 31, No. 13, May 1, 1992, pp2284-2290 “Aberration analysis in aerial images formed by lithographiclenses”, Wolfgang Freitag et al., and in Japanese Patent ApplicationLaid-open No. 2002-22609.

As is described in detail, according to computer system 10 related tothe embodiment, when the first mode previously described is selected,the second communications server 930 calculates the optimal adjustmentamount of the adjustment unit under the target exposure condition, basedon the adjustment information of the above adjustment unit and theinformation related to the image forming quality of the projectionoptical system such as the wavefront aberration under the referenceexposure condition (reference ID). In this case, the relation betweenthe adjustment information of the above adjustment unit and the imageforming quality of the projection optical system such as the wavefrontaberration under the reference exposure condition is known, and when theadjustment is performed, the image forming quality of the projectionoptical system is supposed to be accurate. Accordingly, the optimaladjustment amount under the target exposure condition, which iscalculated based on the adjustment information of the above adjustmentunit and the wavefront aberration of the projection optical system underthe reference exposure condition, will have high accuracy. In addition,based on the calculated adjustment amount, the second communicationsserver 930 adjusts the adjustment unit referred to earlier via the firstcommunications server 920. Accordingly, with computer system 10 relatedto the embodiment, it is possible to swiftly optimize the image formingstate of a projected image of the reticle pattern by projection opticalsystem PL on wafer W under any target exposure condition.

In the embodiment, the second communications 930 is to adjust theadjustment unit, based on the calculation results of the optimaladjustment amount. The second communications server 930, however, doesnot necessarily have to perform the adjustment operation. That is, thesecond communications server 930 may only perform the calculation of theadjustment amount. Even in such a case, by transmitting the informationon the calculated adjustment amount to the first communications server920, exposure apparatus 922, or the operator of such equipment or thelike such as through e-mail, the adjustment unit can be adjusted basedon the information in a manner similar to the one described in the aboveembodiment by the first communications server 920 or exposure apparatus922 themselves, or in response to the instructions from the operator.And, even in such a case, it is possible to swiftly optimize the imageforming state of a projected image of the reticle pattern by projectionoptical system PL on wafer W under any target exposure condition, as isdescribed in the above embodiment.

In this case, since the information related to the image forming qualityonly has to be basic information when calculating the optimal adjustmentamount of the adjustment unit under the target exposure condition, alongwith the adjustment information of the adjustment unit, it may containvarious kinds of information. That is, the information related to theimage forming quality may include information on the wavefrontaberration of the projection optical system that has been adjusted underthe reference exposure condition as in the embodiment described above.Or, it may include information on the wavefront aberration of thestand-alone projection optical system as well as information on theimage forming quality of the projection optical system under thereference exposure condition. In the latter case, information on thewavefront aberration of the projection optical system after adjustmentunder the reference exposure condition may be calculated from the imageforming quality, using the estimation method of the wavefront aberrationpreviously described.

In addition, according to computer system 10 related to the embodiment,when the second mode previously described is selected, the secondcommunications server 930 calculates the optimal adjustment amount ofthe adjustment unit under the target exposure condition, based on theadjustment information of the above adjustment unit and the imageforming quality of the projection optical system such as the actualmeasurement data on wavefront aberration under a predetermined targetcondition. That is, because the optimal adjustment amount of theadjustment unit under the target exposure condition is calculated basedon actual measurement data of the wavefront aberration of the projectionoptical system measured under the target exposure condition, theadjustment amount can be accurately calculated.

In addition, the second communications server 930 adjusts the adjustmentunit described earlier via the first communications server 920, based onthe adjustment amount calculated in the second mode. Accordingly, withcomputer system 10 related to the embodiment, it is possible to swiftlyoptimize the image forming state of a projected image of the reticlepattern by projection optical system PL on wafer W under any targetexposure condition. Since the adjustment amount calculated in this caseis based on actual measurement values, the accuracy is the same orbetter than the case in the first mode.

In this case, as the actual measurement data, any kind of data may beused as long as it may be the base when calculating the optimaladjustment amount of the adjustment unit under the target exposurecondition, along with the adjustment information of the adjustment unit.For example, the actual measurement data may include the actualmeasurement data of the wavefront aberration under the target exposurecondition as in the embodiment. The present invention, however, is notlimited to this, and the actual data may also include the actualmeasurement data of any image forming quality under the target exposurecondition. Even in such a case, the wavefront aberration can be obtainedby simple calculation, using the actual measurement data of the imageforming quality and the Zernike Sensitivity Chart (ZS file) previouslydescribed.

In addition, in the embodiment, the second communications server 930makes the Zernike Sensitivity Chart under the target exposure conditionby interpolation calculation, based on Zernike Sensitivity Charts undera plurality of reference exposure conditions. Therefore, even when theZernike Sensitivity Chart under the target exposure condition is notprepared in advance, it can be swiftly obtained by interpolationcalculation using the Zernike Sensitivity Charts under a plurality ofreference exposure conditions.

In addition, according to computer system 10 related to the embodiment,wavefront aberration measuring instrument 80 in exposure apparatus 922self-measures the wavefront of projection optical system PL. The firstcommunications server 920 transmits the measurement results of thewavefront of projection optical system PL measured by wavefrontaberration measuring instrument 80 to the second communications server930 via a communications channel. The second communications server 930uses the measurement results of the wavefront to control the adjustmentunit previously described. Accordingly, the image forming quality ofprojection optical system PL is adjusted with good accuracy using theinformation of the wavefront on the pupil plane of the projectionoptical system, that is, the overall information of the wavefront thatpasses through the pupil plane. As a consequence, the image formingstate of the pattern by the projection optical system is adjusted to anoptimum. In this case, the second communications server 930 can bearranged at a position away from exposure apparatus 922 and the firstcommunications server 920 joined to exposure apparatus 922. In such acase, the image forming quality of projection optical system PL, and inturn the image forming state of the pattern by projection optical systemPL can be adjusted with high precision by remote control.

In addition, when an intranet system as in FIG. 1 is built within anexposure apparatus maker, the first communications server 920 isinstalled, for example, in a clean room side of a research developmentdepartment, such as in a place where the exposure apparatus is built andadjusted (hereinafter referred to as a ‘site’), and the secondcommunications server 930 is installed in a laboratory away from thesite. Then, the engineer at the site sends the measurement of thewavefront aberration previously described and the information onexposure conditions of the exposure apparatus at the experimental stage(including pattern information) to the second communications server 930at the laboratory side via the first communications server 920. And, theengineer at laboratory side remotely performs automatic correction ofthe image forming quality of projection optical system PL of exposureapparatus 922 based on the information received, using the secondcommunications server 930 in which a software program designed by theengineer is installed in advance. And then, by receiving the measurementresults of the wavefront aberration of the projection optical systemwhose image forming quality has been adjusted, the results of theadjustment of the image forming quality can be confirmed, which may alsobe useful during the development stage when developing software.

The processing algorithm of the second communications server describedin the above embodiment is a mere example, and it is a matter of coursethat the image forming state adjusting system in the present inventionis not limited to this.

For example, specifying the weight (weight of image forming quality,weight at each evaluation point within the field) previously described,specifying the target (target value of the image forming quality at eachevaluation point within the field), and specifying the optimizing fieldrange do not necessarily have to be performed. This is because these canbe specified in advance as a default setting, as is previouslydescribed.

Due to similar reasons, specifying permissible values and restraintconditions do not necessary have to be performed.

On the other hand, other functions that have not been described so farmay be added. For example, specifying the evaluation mode may be added.More specifically, for example, specifying the evaluation method such asthe absolute value mode or the maximum minimum width mode (per axis,all) may be added. In this case, because the optimizing calculationitself is performed with the absolute value of the image forming qualityas the target at all times, the absolute value mode is to be a defaultsetting, and the maximum minimum width mode is to be optional.

To be more specific, for example, with distortion whose average valuesmay be deducted as offset in both the X-axis direction and Y-axisdirection, the maximum minimum width mode (range/offset per axis) can bespecified. In addition, with TFD (total focus difference due to in-planeevenness in astigmatism and curvature of field) or the like whoseaverage value of the entire XY plane is deducted as offset, the maximumminimum width mode (range/total offset) can be specified.

The maximum minimum width mode will be required when the measurementresults are evaluated. That is, when the decision is made whether thewidth is within a permissible value range, and the width turns out to beoff the permissible value range, the optimizing calculation can beperformed again with different calculation conditions (such as weight).

In addition, in the above embodiment, the necessary ZS files were madeby the interpolation method previously described, however, the presentinvention is not limited to this. For example, the ZS files may be madewhen necessary in methods other than the interpolation method, or moreZS files may be prepared in advance and the ZS file that has the closestconditions may be selected and used as the ZS file.

In addition, in the above embodiment, in the case of mode 1, wavefrontaberration that has been calculated under the reference ID is used,while in the case of mode 2, wavefront aberration that has been actuallymeasured is used, and in the case of mode 3, wavefront aberration datasimilar to mode 1 is used. However, for example, wavefront aberrationthat has been actually measured may be used in the case of mode 3. Thatis, the 12 types of aberration previously described may be obtained bycalculation under various exposure conditions based on the wavefrontaberration actually measured, and when the best exposure condition isdecided based on the calculation results, a more accurate best exposurecondition can be decided because the actual measurement data has beenused as the basic data.

In addition, in the cases of mode 1 and mode 3, instead of usingwavefront aberration that has been calculated under the reference ID,wavefront aberration that has been actually measured may be used. Thepoint is that the data used on the optimizing calculation or the like iswavefront aberration data.

In addition, instead of the wavefront aberration, actual measurementdata on individual image forming quality can be used as is previouslydescribed. However, such measurement of the image forming quality maysimply be detecting the pattern image of the image with an aerial imagemeasuring instrument whose photodetection surface is provided on Z tiltstage 58, or transferring the reticle pattern onto the wafer, detectingthe transferred image (such as a latent image or a resist image), andobtaining the image forming quality from the detection results.

In addition, in the above embodiment, three modes from mode 1 to mode 3can be set in the second communications server. The modes, however, mayalso be set only to mode 1, mode 2, modes 1 and 2, modes 1 and 3, andmodes 2 and 3.

In the description so far, from the viewpoint of avoiding complication,no particular reference is made to the point that the image formingquality of the projection optical system changes due to an atmosphericpressure change of the environment in which the exposure apparatus isinstalled and the quantity of energy irradiated on the projectionoptical system, that is, the so-called atmospheric pressure change andthe so-called irradiation fluctuation of the image forming quality.However, in the above embodiment, such points may be taken intoconsideration.

For example, basic data on atmospheric pressure change can be obtainedby monitoring the relation between the change of atmospheric pressure inthe environment in which the projection optical system is arranged andthe image forming quality (for example, wavefront aberration), or byhousing the projection optical system in a decompression chamber andmeasuring the change in the image forming quality while changing theinner pressure of the decompression chamber. In addition, basic data onirradiation fluctuation can be obtained by actually measuring the changein the image forming quality when the illumination light is irradiatedon the projection optical system. As a matter of course, these basicdata can also be obtained by performing a highly precise opticalsimulation.

Meanwhile, in the embodiment previously described, when the database ismade for the wavefront aberration variation table under the reference IDor the like, reference values can be assumed for such atmosphericpressure and irradiation quantity, and the database such as thewavefront aberration variation table can be made taking the values intoconsideration by the simulation referred to earlier. Then, for example,when mode 1 previously described is selected, as a premise for using thecalculated wavefront aberration under the reference ID, the secondcommunications server 930 loads the measurement data of a sensor thatmeasures the atmospheric pressure in chamber 11 (or in the clean room)of exposure apparatus 922 subject to adjustment amount calculation andthe irradiation record in the log data that main controller 50 ofexposure apparatus 922 collects via the first communications server 920,when it performs the optimizing of the image forming state. Then, basedon such data, the second communications server 930 calculates thefluctuation amount of the atmospheric pressure and irradiation quantityfrom a reference atmospheric pressure and a reference irradiationquantity under the reference ID. And based on such calculation results,the second communications server 930 calculates the atmospheric pressureand irradiation quantity of the image forming quality of the projectionoptical system, and taking the calculated results into consideration,performs the optimizing process using the calculated wavefrontaberration under the reference ID in mode 1 previously described.

For example, the optimal condition under the target exposure conditionis not directly calculated based on data such as the wavefrontaberration variation table under the reference ID (the exposurecondition serving as a reference), but is calculated by making a thirdexposure condition that either has at least a different atmosphericpressure or a different illumination light quantity of the projectionoptical system compared to the reference ID stand between the referenceID and the target exposure condition, obtaining the data on wavefrontaberration variation table or the like under the third exposurecondition (a more accurate data on wavefront aberration variation tableor the like, which is various data such as the wavefront aberrationvariation table or the like under the reference ID that has beencorrected so that the atmospheric change and irradiation fluctuation inthe image forming quality of the projection optical system are takeninto consideration), and then calculating the optimal condition underthe target exposure condition based on the data that has been obtained.

Not only in the case of mode 3, but also in mode 2, the aboveatmospheric change and irradiation fluctuation in the image formingquality of the projection optical system may also similarly be takeninto consideration. This can also be said for the modified example thatwill be described later in the description.

The various changes described above in the processing algorithm of thesecond communications server can be easily made by making changes to thesoftware.

The system configuration described in the above embodiment is a mereexample, and the image forming state adjusting system related to thepresent invention is not limited to this. For example, as in thecomputer system shown in FIG. 22, the system may employ a configurationthat comprises a public line 916 as a part of its communication channel.

Computer system 10′ shown in FIG. 22 comprises a lithographic system912′ set up in a semiconductor manufacturing site of a devicemanufacturer (hereinafter referred to as ‘maker A’ as appropriate) thatuses device manufacturing equipment such as an exposure apparatus, and acomputer system 914 of an exposure apparatus maker (hereinafter referredto as ‘maker B’ as appropriate) joined to lithographic system 912′ viathe communication channel that has a public line 916 as a part of itschannel.

Lithographic system 912′ comprises a first communications server 920, afirst to third exposure apparatus 922 ₁ to 922 ₃, and a firstauthentication proxy server 924 connecting reciprocally via a LAN 918.

The first communications server 920 and each of the first to thirdexposure apparatus 922 ₁ to 922 ₃ are to have an assigned address, AD1to AD4, respectively.

The first authentication proxy server 924 is provided in between LAN 918and public line 916, and in this case, functions as a kind of afirewall. That is, the first authentication proxy server 924 secures thecommunications of data flowing through LAN 918 from the outside, and byallowing access only to information from the outside that has theaddresses AD1 to AD4 and blocking other information, it protects LAN 918from external attacks.

Computer system 914 comprises a second authentication proxy server 928and a second communications server 930 connecting reciprocally via a LAN929. In this case, an address AD5 is assigned to the secondcommunications server 930 for identification.

Similar to the first authentication proxy server 924, the secondauthentication proxy server 928 functions as a kind of a firewall thatsecures the communications of data flowing through LAN 929 from theoutside, and protects LAN 929 from external attacks.

In system 10′ in FIG. 22, when data is transmitted outside the systemfrom the first to third exposure apparatus 922 ₁ to 922 ₃, it istransmitted via the first communications server 930 and the firstauthentication proxy server 924, while data transmitted from the outsideto the first to third exposure apparatus 922 ₁ to 922 ₃ goes via thefirst authentication proxy server 924 and then directly to the first tothird exposure apparatus, or via the first authentication proxy server924 and the first communications server 920.

System 10′ in FIG. 22 is suitable for times such as periodic maintenancewhen a service technician or the like who is visiting maker A onbusiness adjusts the image forming state of the projected image of apattern on the object in the exposure apparatus, using the optimizingprogram previously described which is installed in the secondcommunications server 930.

Besides the above description, the following operation is possible withthe system configuration in FIG. 22. More particularly, in the automaticadjustment of the adjustment unit previously described, there may becases when the aberration is difficult to correct. In such a case, theservice technician can perform the wavefront aberration at the site(maker A side) and send the data to the second communications server 930via the first communications server 920 and public line 916. Then, askilled engineer of maker B can retrieve the measurement data of thewavefront from the hard disc of the second communications server 930 andshow it on the display, analyze the contents, and figure out theproblems. And when the engineer finds an aberration that is difficult tocorrect by automatic adjustment, instructions on precise countermeasurescan be input from the keyboard or the like of the second communicationsserver 930 and transmitted so that can be shown on the screen of displayunit 44 of exposure apparatus 922. Then, the service technician at makerA can perform fine adjustment on the lens assembly based on the contentsdisplayed, which allows the projection optical system to be adjusted ina short period of time.

In addition, in the above embodiment and the modified example in FIG.22, the case has been described when the optimizing program that hasbeen described earlier is stored within the second communications server930. However, the present invention is not limited to this, and a CD-ROMin which the optimizing program and the database that goes with theprogram are stored may be set in the CD-ROM of the first communicationsserver 920, and the optimizing program and the database that goes withthe program may be installed or copied into the storage unit such as thehard disc of the first communications server 920. Such an arrangementallows the optimizing processing to be performed, by the firstcommunications server 920 simply receiving the information from exposureapparatus 922.

In addition, as is previously described, in the hard disc or the like ofthe first communications server 920, target information that is to beachieved in the first to third exposure apparatus 922 ₁ to 922 ₃ isstored, such as resolution, practical minimum line width (device rule),wavelength of illumination light EL (such as center wavelength andwavelength width), information on the pattern subject to transferring,and any other information related to the projection optical system thatdecides the quality of exposure apparatus 922 ₁ to 922 ₃ that can becomea target value. In addition, in the hard disc or the like of the firstcommunications server 920, target information related to the exposureapparatus that will be used, such as information on the pattern thatwill be used, is also stored as target information.

Accordingly, the best exposure condition can be automatically set, bysetting the default setting of the mode to mode 3 and making a change inthe software so that the various condition settings that the operatorperforms in mode 3 is performed by the first communications server 920itself instead.

Or, the CD-ROM in which the optimizing program and the database thatgoes with the program can be set in drive unit 46 of exposure apparatus922, and the optimizing program and the database that goes with theprogram may be installed or copied into storage unit 42 such as the harddisc from the CD-ROM drive. When such an arrangement is employed,exposure apparatus 922 will be able to perform the optimizing processingthat has been described on its own. Instead of the operator inputtingthe pattern information, the exposure apparatus may obtain theinformation from a host computer at the device manufacturing site ofmaker A or by reading a barcode or a two-dimensional code provided inthe reticle on which the pattern to be transferred to the wafer isformed, and automatically adjust projection optical system PL, withouthaving an operator or a service technician intervening. In this case,main computer 50 will constitute the processing unit that controls theadjustment previously described.

That is, main controller 50 performs the mode 1 processing (includingthe decision making) and calculates the optimal adjustment amount of theadjustment unit under the target exposure condition based on adjustmentinformation on the adjustment unit and information related to the imageforming quality of the projection optical system such as wavefrontaberration under the reference exposure condition (reference ID), andthen controls the adjustment unit based on the calculated adjustmentamount. As a result, for similar reasons described earlier in thedescription, the image forming state of the projected image of a patternon the wafer under any target exposure condition is substantiallyautomatically optimized.

In this case, the information related to the image forming quality caninclude various types of information. For example, it may includeinformation on wavefront aberration of the projection optical systemthat has already been adjusted under the reference ID, or it may includeinformation on the stand-alone wavefront aberration of the projectionoptical system and the image forming quality of the projection opticalsystem under the reference ID.

In addition, main controller 50 performs the mode 2 processing andcalculates the optimal adjustment amount of the adjustment unit underthe target exposure condition based on adjustment information on theadjustment unit and actual measurement data of the image forming qualityof the projection optical system (wavefront aberration or other types ofaberration) under a predetermined target exposure condition, and thencontrols the adjustment unit based on the calculated adjustment amount.In this case, for similar reasons described earlier in the description,the image forming state of the projected image of a pattern on the waferunder any target exposure condition is substantially automaticallyoptimized. And, in this case, the adjustment unit is controlled based ona more accurate adjustment amount than that of the case in mode 1.

In the above embodiment, when using the actual measurement data of thewavefront aberration as the actual measurement data of the image formingquality of the projection optical system, the wavefront aberrationmeasurement can be performed using, for example, a wavefront aberrationmeasuring unit. As such a wavefront aberration measuring unit, a unitthat is shaped so that it can be totally exchanged with the wafer holdermay be used. In such a case, the wavefront aberration measuring unit canbe automatically carried, using a carriage system (such as a waferloader) that loads and unloads the wafer or the wafer holder onto waferstage WST (Z tilt stage 58). The wavefront aberration measuring unitloaded onto the wafer stage, such as wavefront aberration measuringinstrument 80 does not have to be completely assembled into the waferstage, and only a part of it may be arranged within the wafer stage withthe remaining arranged outside. Furthermore, in the above embodiment,the aberration of the photodetection optical system of wavefrontaberration measuring instrument 80 is ignored, however, the wavefrontaberration of the projection optical system can be decided taking suchwavefront aberration into consideration. In addition, on wavefrontaberration measurement, when a measurement reticle disclosed in forexample, the U.S. Pat. No. 5,978,085 referred to earlier, is used, thepositional deviation of the latent image of a measurement patterntransferred and formed on the resist layer on the wafer with respect tothe latent image of a reference pattern may be detected, for example, byalignment system ALG in the exposure apparatus. In the case of detectingthe latent image of the measurement pattern, a photoresist may be usedas the sensitive layer of an object such as the wafer, or a magnetoptical material. Furthermore, the exposure apparatus and coaterdeveloper may be inline connected so that the resist image obtained bydeveloping an object such as the wafer on which the measurement patternis transferred, or furthermore, the etched image obtained by the etchingprocess, may be detected by alignment system ALG in the exposureapparatus. In addition, a measurement unit may be provided separately,apart from the exposure apparatus to detect the transferred images (suchas the latent image or the resist image) of the measurement pattern, andthe results may be sent to the exposure apparatus via LAN or Internet,or by radio communication. And, in addition to the description so far,the mode setting in the optimizing program referred to earlier is to bearranged so that mode 1 is selected by the default setting. Such devisedideas allow the first communications server to perform the automaticadjustment of the image forming quality of projection optical system PLdescribed earlier automatically, without any intervening by an operatoror a service technician. Similarly, the exposure apparatus can performthe automatic adjustment of the image forming quality of projectionoptical system PL previously described by itself also by having theoptimizing program installed into storage unit 42 in exposure apparatus922, without any intervening by an operator or a service technician.

Besides such details, the first communications server 920 and the secondcommunications server 930 may be joined by a radio link.

In the above embodiment and the modified example, the case has beendescribed where optimizing is performed on the 12 types of image formingquality, however, the type (number) of image forming quality is notlimited to this, and by changing the type of exposure condition subjectto optimizing, the number of image forming quality to be optimized maybe increased or decreased. For example, the type of image formingquality included as an evaluation quantity in the Zernike SensitivityChart simply has to be changed.

In addition, in the above embodiment and the modified example, the casehas been described where all the coefficients of the 1^(st) to n^(th)terms in the Zernike polynomial are used, however, the coefficient doesnot have to be used in at least one term of the 1^(st) to n^(th) terms.For example, the corresponding image forming quality may be adjusted asusual, without using the coefficients of the 2^(nd) to 4^(th) terms. Inthis case, when the coefficients of the 2^(nd) to 4^(th) terms are notused, the adjustment of the corresponding image forming quality may beperformed by adjusting the position of at least one of movable lenses 13₁ to 13 ₅ described earlier in directions of three degrees of freedom,or it may be performed by adjusting the Z position and the inclinationof wafer W (Z tilt stage 58).

In addition, in the above embodiment and the modified example, the casehas been described where the wavefront measuring unit performscalculation up to the 81^(st) term while the wavefront aberrationmeasuring instrument performs calculation up to the 37^(th) term, or theterms of 82 and over are calculated, however, the present invention isnot limited to this. Similarly, the wavefront aberration variation tablepreviously described is not limited to the ones on the 1^(st) to 37^(th)terms.

Furthermore, in the above embodiment and the modified example, the casehas been described where optimizing is performed using the Least SquaresMethod or Damped Least Squares Method, however, the following methodscan also be used: (1) gradient methods such as the Steepest DecentMethod or the Conjugate Gradient Method, (2) Flexible Method, (3)Variable by Variable Method, (4) Orthonomalization Method, (5) AdaptiveMethod, (6) Quadratic Differentiation, (7) Global Optimization bySimulated annealing, (8) Global Optimization by Biological evolution,and (9) Genetic Algorithm (refer to U.S. Patent Application No.2001/0053962).

In each of the above embodiments, the case has been described where aLAN, or a LAN and a public line or other signal cables are used as thecommunication channel, however, the present invention is not limited tothis, and the signal cables and the communication channel may either bewired or wireless.

In addition, in the above embodiment and the modified example, the casehas been described where σ value (coherence factor) and annular ratioare used as the information on illumination condition in normalillumination and annular illumination, respectively. In the annularillumination, however, in addition to, or instead of the annular ratio,the inside diameter or the outside diameter may be used. Or, in themodified illumination such as in quadrupole illumination (also calledSHRINC or multipole illumination), because the dose of the illuminationdose distribution on the pupil plane of the illumination optical systemincreases in a plurality of partial areas whose dose centroid are set atpositions of a substantially equal distance from the optical axis of theillumination optical system, the positional information of the pluralityof partial areas (dose centroid) on the pupil plane of the illuminationoptical system (for example, the coordinate values in a coordinatesystem whose origin is the optical axis on the pupil plane of theillumination optical system), the distance between the plurality ofpartial areas (dose centroid) and the optical axis of the illuminationoptical system, and the size of the partial area (which corresponds tothe σ value) may also be used as the information.

Furthermore, in the above embodiment and the modified example, the casehas been described where the image forming quality is adjusted by movingthe optical elements of projection optical system PL. The image formingquality adjustment mechanism, however, is not limited to the drivemechanism of the optical elements, and in addition to, or instead of thedrive mechanism, mechanisms may be used that changes the pressure of gasin between the optical elements of projection optical system PL, movesor inclines reticle R in the optical axis direction of the projectionoptical system, or changes the optical thickness of the plane-parallelplate disposed in between the reticle and the wafer. However, in such acase, the number of degrees of freedom may be changed in the aboveembodiment and the modified example.

In addition, in the above embodiment and the modified example, the casehas been described where exposure apparatus 922 is provided in pluralsand the second communications server 930 shares a link with theplurality of exposure apparatus 922 ₁ to 922 ₃ via a communicationchannel. However, the present invention is not limited to this, and as amatter of course, the exposure apparatus may be singular.

In the above embodiment, the case has been described where a stepper isused as the exposure apparatus. The present invention, however, is notlimited to this, and a scanning exposure apparatus that transfers apattern of a mask onto an object while synchronously moving the mask andthe object, such as the one disclosed in, for example, U.S. Pat. No.5,473,410, may also be used.

Furthermore, in the above embodiment and the modified example, the casehas been described where the plurality of exposure apparatus used hasthe same configuration. However, an exposure apparatus whose wavelengthof illumination light EL is different may also be used together, or anexposure apparatus that has a different configuration, such as a statictype exposure apparatus (such as a stepper) and a scanning type exposureapparatus (such as a scanner) may be combined. In addition, a part ofthe plurality of exposure apparatus may be an exposure apparatus thatuses charged particle beams such as an electron beam or an ion beam.Also, an immersion exposure apparatus that has liquid filled in betweenprojection optical system PL and the wafer whose details are disclosedin, for example, the International Publication WO99/49504, may be used.

The usage of the exposure apparatus in this case is not limited to theexposure apparatus used for manufacturing semiconductors, but it canalso be widely applied to an exposure apparatus used for transferring aliquid crystal display device pattern onto a square glass plate whenmanufacturing liquid crystal displays, or to an exposure apparatus usedfor manufacturing display devices such as a plasma display or an organicEL, pick-up devices (such as a CCD), thin film magnetic heads,micromachines, and DNA chips. In addition, the present invention canalso be applied not only to an exposure apparatus used for manufacturingmicrodevices such as a semiconductor, but also to an exposure apparatusthat transfers a circuit pattern onto a glass substrate or a siliconwafer in order to manufacture a reticle or a mask used in an opticalexposure apparatus, an EUV exposure apparatus, and X-ray exposureapparatus, and an electron beam exposure apparatus.

In addition, the light source of the exposure apparatus in the aboveembodiment is not limited to the ultraviolet pulse light source such asthe F₂ laser, ArF excimer laser, and KrF excimer laser, and a continuouslight source as in, for example, an extra-high pressure mercury lampthat emits an emission line such as a g-line (wavelength 436 nm) or ani-line (wavelength 365 nm) can also be used. Furthermore, asillumination light EL, X-ray may also be used, especially EUV light.

In addition, a harmonic wave may be used that is obtained by amplifyinga single-wavelength laser beam in the infrared or visible range emittedby a DFB semiconductor laser or fiber laser, with a fiber amplifierdoped with, for example, erbium (or both erbium and ytteribium), and byconverting the wavelength into ultraviolet light using a nonlinearoptical crystal. Also, the magnification of the projection opticalsystem is not limited to a reduction system, and an equal magnificationor a magnifying system may be used. Furthermore, the projection opticalsystem is not limited to a refraction system, and a catadioptric systemthat has reflection optical elements and refraction optical elements maybe used as well as a reflection system that uses only reflection opticalelements. When the catadioptric system or the reflection system is usedas projection optical system PL, the image forming quality of theprojection optical system is adjusted by changing the position or thelike of the reflection optical elements (such as a concave mirror or areflection mirror) that serve as the movable optical elements previouslydescribed. In addition, when especially the Ar₂ laser beam or the EUVlight or the like is used as illumination light EL, projection opticalsystem PL can be a total reflection system that is made up only ofreflection optical elements. However, when the Ar₂ laser beam, the EUVlight, or the like is used, reticle R also needs to be a reflective typereticle.

Incidentally, semiconductor devices are made undergoing the followingsteps: a device function/performance designing step, a reticle makingstep where a reticle is made based on the designing step, a wafer makingstep where a wafer is made from silicon material, a transferring stepwhere the pattern of the reticle is transferred onto the wafer by theexposure apparatus in the embodiment, a device assembly step (includingthe dicing process, bonding process, and packaging process), and aninspection step. According to the device manufacturing method, becauseexposure is performed in a lithographic process using the exposureapparatus in the above embodiment, the pattern of reticle R istransferred onto wafer W via projection optical system PL whose imageforming quality is adjusted according to the subject pattern, or whoseimage forming quality is adjusted with high precision based on themeasurement results of the wavefront aberration, and therefore it ispossible to transfer fine patterns onto wafer W with high overlayaccuracy. Accordingly, the yield of the devices as final products isimproved, which makes it possible to improve its productivity.

While the above-described embodiment of the present invention is thepresently preferred embodiment thereof, those skilled in the art oflithography systems will readily recognize that numerous additions,modifications, and substitutions may be made to the above-describedembodiments without departing from the spirit and scope thereof. It isintended that all such modifications, additions, and substitutions fallwithin the scope of the present invention, which is best defined by theclaims appended below.

1. An exposure apparatus that forms a pattern on an object via a projection optical system, said apparatus comprising: a setting device that sets an exposure condition whose a setting value is variable in at least one setting information among a plurality of setting information, related to a projection condition of a pattern subject to projection by said projection optical system; an adjustment system that adjusts an imaging state of a pattern by said projection optical system; and a calculating device which decides optimal adjustment amounts of said adjustment system under a plurality of exposure conditions that have different setting values in said at least one setting information to optimize said imaging state for each exposure condition, respectively, based on information related to wavefront aberration of said projection optical system and a plurality of Zernike Sensitivity Charts that correspond to said plurality of exposure conditions and are different from each other, the calculating device making at least one of said plurality of Zernike Sensitivity Charts by interpolation calculation based on different Zernike Sensitivity Charts from said at least one Zernike Sensitivity Chart.
 2. The exposure apparatus in claim 1 wherein said information related to wavefront aberration is estimated from information on image forming property of said projection optical system.
 3. The exposure apparatus in claim 1 wherein said information related to wavefront aberration is obtained from positional information of a pattern image within an image plane of said projection optical system.
 4. The exposure apparatus in claim 1 wherein a restraint condition with respect to an adjustment amount of said adjustment system is used to decide said optimal adjustment amounts.
 5. The exposure apparatus in claim 4 wherein information related to a permissible error value of said imaging state is used to decide said optimal adjustment amounts.
 6. The exposure apparatus in claim 5 wherein a wavefront aberration variation table, that denotes a relation between an adjustment amount of said adjustment system and a change in coefficients of terms in a Zernike polynomial, is used to decide said optimal adjustment amounts.
 7. The exposure apparatus in claim 6 wherein said Zernike Sensitivity Chart denotes a relation between said forming state and coefficients of terms in said Zernike polynomial.
 8. The exposure apparatus in claim 1 wherein said optimal adjustment amounts are calculated using a weighting function that performs weighting on at least one term of a Zernike polynomial.
 9. The exposure apparatus in claim 8 wherein said projection condition includes an illumination condition of said pattern.
 10. An exposure method of forming a pattern on an object via a projection optical system, comprising: deciding optimal adjustment amounts of an adjustment system, which adjusts an imaging state of a pattern by said projection optical system, under a plurality of exposure conditions that have different setting values in at least one setting information among a plurality of setting information, related to a projection condition of a pattern subject to projection by said projection optical system to optimize said imaging state for each exposure condition, respectively, based on information related to wavefront aberration of said projection optical system and a plurality of Zernike Sensitivity Charts that correspond to said plurality of exposure conditions and are different from each other, wherein exposures under said plurality of exposure conditions are performed based on said decided optimal adjustment amounts, and at least one of said plurality of Zernike Sensitivity Charts is made by interpolation calculation based on different Zernike Sensitivity Charts from said at least one Zernike Sensitivity Chart.
 11. A device manufacturing method comprising: exposing an object by said exposure method according to claim 10; and processing the exposed object for manufacturing a device.
 12. The exposure method in claim 10 wherein said information related to wavefront aberration is estimated from information on image forming property of said projection optical system.
 13. The exposure method in claim 10 wherein said information related to wavefront aberration is obtained from positional information of a pattern image within an image plane of said projection optical system.
 14. The exposure method in claim 10 wherein a restraint condition with respect to an adjustment amount of said adjustment system is used to decide said optimal adjustment amounts.
 15. The exposure method in claim 14 wherein information related to a permissible error value of said imaging state is used to decide said optimal adjustment amounts.
 16. The exposure method in claim 15 wherein a wavefront aberration variation table, that denotes a relation between an adjustment amount of said adjustment system and a change in coefficients of terms in a Zernike polynomial, is used to decide said optimal adjustment amounts.
 17. The exposure method in claim 16 wherein said Zernike Sensitivity Chart denotes a relation between said forming state and coefficients of terms in said Zernike polynomial.
 18. The exposure method in claim 10 wherein said optimal adjustment amounts are calculated using a weighting function that performs weighting on at least one term of a Zernike polynomial.
 19. The exposure method in claim 18 wherein said projection condition includes an illumination condition of said pattern.
 20. An information storage medium that stores a program and can be read by a computer connected to an exposure apparatus that forms a pattern on an object via a projection optical system and includes an adjustment system to adjust an imaging state of the pattern, said program making said computer execute a procedure of: deciding optimal adjustment amounts of an adjustment system, which adjusts an imaging state of a pattern by said projection optical system, under a plurality of exposure conditions that have different setting values, in at least one setting information among a plurality of setting information, related to a projection condition of a pattern subject to projection by said projection optical system to optimize said imaging state for each exposure condition, respectively, in response to input of information related to wavefront aberration of said projection optical system and a plurality of Zernike Sensitivity Charts that correspond to said plurality of exposure conditions and are different from each other, wherein exposures under said plurality of exposure conditions are performed based on said decided optimal adjustment amounts, and at least one of said plurality of Zernike Sensitivity Charts is made by interpolation calculation based on different Zernike Sensitivity Charts from said at least one Zernike Sensitivity Chart.
 21. The information storage medium of claim 20 wherein said information related to wavefront aberration is estimated from information on image forming property of said projection optical system.
 22. The information storage medium of claim 20 wherein said information related to wavefront aberration is obtained from positional information of a pattern image within an image plane of said projection optical system.
 23. The information storage medium in claim 20 wherein a restraint condition with respect to an adjustment amount of said adjustment system is used to decide said optimal adjustment amounts.
 24. The information storage medium in claim 23 wherein information related to a permissible error value of said imaging state is used to decide said optimal adjustment amounts.
 25. The information storage medium in claim 24 wherein a wavefront aberration variation table, that denotes a relation between an adjustment amount of said adjustment system and a change in coefficients of terms in a Zernike polynomial, is used to decide said optimal adjustment amounts.
 26. The information storage medium in claim 25 wherein said Zernike Sensitivity Chart denotes a relation between said forming state and coefficients of terms in said Zernike polynomial.
 27. The information storage medium in claim 20 wherein said optimal adjustment amounts are calculated using a weighting function that performs weighting on at least one term of a Zernike polynomial.
 28. The information storage medium in claim 27 wherein said projection condition includes a illumination condition of said pattern. 